Metsis:Finally a warning. Verbs with iĝi are always in active voice in Esperanto, even if some speakers try to use it in a sort of passive voice, e.g. libro legiĝas is not correct, because a book cannot read itself.

Ivo Lapenna, eksprezidanto de la UEA, (kaj aliaj Esperantistoj) opinias malsame:

Tekstaro:iliaj poemoj restas en tirkestoj, aŭ legiĝas en la grupo

Zamenhof mem:

Kion Li detruas, tio ne rekonstruiĝas.

Evidente tio, kion Li detruas, ne rekonstruas sin mem, sed ankaŭ ĉi tie rekonstruiĝas estas pseŭdopasivo.

Nornen,

Jes, I am aware, that some use iĝi that way, but…

1. It's an exception

Only iĝi verbs with a verbal character root of transitive verbs can have a passive voice character. That is, malpuriĝi cannot be understood to have a passive voice character (non-verbal root). Nor cannot mortiĝi be understood in such a way (intransitive verbal root).

To insist that Esperanto has no exceptions is BS, as we all know, but there is a strong tendency to avoid them. By using some iĝi verbs in role of passive voice we create an exception, that is easily avoidable by ,say, oni passive.
 

• iliaj poemoj restas en tirkestoj, aŭ legiĝas en la grupo → …aŭ oni legas ilin en la grupo.

2. What passive voice means

This is more a philosophical argument. To my understanding there are two ways to perceive, what passive voice means. It can either
 

• impersonate the action: Ri donis al mi ringon → Oni donis ringon al mi or
  
• describe a change of the state of an object: Ri donis al mi ringon → Ringo estas donita de ri al mi.

I admit, that because my of denaska lingvo I understand passive voice to mean the former (oni-passive), while the later (esti-passive) is alien to me (especially the agent part).

Therefore I have hard time to grasp a sentence like La libro legiĝas. Because la libro is in nominative and has no preposition, it must be the subject according to the grammar of Esperanto. The verb legiĝas has the iĝi ending, ah, it becomes read, but by whom or what. Of course by the subject, that's the definition of the subject, so the book becomes read by itself. Being a computer nerd I can imagine a future, when this could happen, but before that I get stumbled. It takes a couple of seconds to decipher, that in the sentence the obvious subject isn't a subject at all, but an object although not marked as one. In other words an exception to the fundamental rules of Esperanto (pun intended).

Metsis:Nornen,

Jes, I am aware, that some use iĝi that way, but…

1. It's an exception

Only iĝi verbs with a verbal character root of transitive verbs can have a passive voice character. That is, malpuriĝi cannot be understood to have a passive voice character (non-verbal root). Nor cannot mortiĝi be understood in such a way (intransitive verbal root).

To insist that Esperanto has no exceptions is BS, as we all know, but there is a strong tendency to avoid them. By using some iĝi verbs in role of passive voice we create an exception, that is easily avoidable by ,say, oni passive.
 

• iliaj poemoj restas en tirkestoj, aŭ legiĝas en la grupo → …aŭ oni legas ilin en la grupo.

2. What passive voice means

This is more a philosophical argument. To my understanding there are two ways to perceive, what passive voice means. It can either
 

• impersonate the action: Ri donis al mi ringon → Oni donis ringon al mi or
  
• describe a change of the state of an object: Ri donis al mi ringon → Ringo estas donita de ri al mi.

I admit, that because my of denaska lingvo I understand passive voice to mean the former (oni-passive), while the later (esti-passive) is alien to me (especially the agent part).

Therefore I have hard time to grasp a sentence like La libro legiĝas. Because la libro is in nominative and has no preposition, it must be the subject according to the grammar of Esperanto. The verb legiĝas has the iĝi ending, ah, it becomes read, but by whom or what. Of course by the subject, that's the definition of the subject, so the book becomes read by itself. Being a computer nerd I can imagine a future, when this could happen, but before that I get stumbled. It takes a couple of seconds to decipher, that in the sentence the obvious subject isn't a subject at all, but an object although not marked as one. In other words an exception to the fundamental rules of Esperanto (pun intended).

As to my logic sense these sentences look pretty good:
Li diris la diagnozon kaj nia lasta espero mortigxis. The hope was killed by his words.
La vesto puritigxis bone. The cleaning of the clothes was easy.
This one from a book translated by Zamenhof:
"Cxu vi vidas tie la grandan arbon?"diris la sorcxistino, montrante arbon, kiu trovigxis apud ili.
This one was took right here, from the grama rules of lernu:
La pordo malfermigxis.
This one from a dictionary:
Rugxigxi de honto.
Let me know if they are wrong and why.

Kara Metsis,

2. What passive voice means

This is more a philosophical argument. To my understanding there are two ways to perceive, what passive voice means. It can either

impersonate the action: Ri donis al mi ringon → Oni donis ringon al mi or
describe a change of the state of an object: Ri donis al mi ringon → Ringo estas donita de ri al mi.

Ofta difino de pasiva konstruaĵo baziĝas sur tiuj kondiĉoj:
1. La pasiva konstruaĵo estas derivita el aktiva konstruaĵo.
2. La subjekto ne estas aganto (agent = A).
3. La konstruaĵo estas markita. (Tio signifas, ke ĝi iel malsamas al aktiva konstruaĵo, eble per vortordo, verba fleksio, noma fleksio de siaj argumentoj, ktp)

La grava afero estas (2). La subjekto ne estas aganto, sed eble suferanto (patient = P) aŭ alia sintaksa rolo.
Ekzemple:
I was hit by a car. (subjekto estas P)
I was given a book. (subjekto estas ricevanto).

Nun ni supozu, ke "legiĝas" ja havas pasivajn ecojn.

Because la libro is in nominative and has no preposition, it must be the subject according to the grammar of Esperanto.

Having nominative case and no preposition is not a sufficient condition for being the subject, but in this example "libro" is indeed the subject.

The verb legiĝas has the iĝi ending, ah, it becomes read, but by whom or what. Of course by the subject, that's the definition of the subject, so the book becomes read by itself.

Here's the problem. The subject of a passive construction is not the agent. Hence the subject of a passive construction never answers the question "who or what did it?".
Take a real passive for instance: La libro estas legata. Again "libro" is the subject and it surely is not the agent, but the theme. According to your argumentation (by whom is it being read? Of course by the subject), "la libro estas legata" means the same thing as "la libro legas", i.e. something (unmentioned) is being read by a book.
I was hit by a car. Something becomes hit, but by whom or what? Not by the subject.
I was given a ring. Something is being given, but by whom or what? Not by the subject.

impersonate the action: Ri donis al mi ringon → Oni donis ringon al mi or
describe a change of the state of an object: Ri donis al mi ringon → Ringo estas donita de ri al mi.

I admit, that because my of denaska lingvo I understand passive voice to mean the former (oni-passive), while the later (esti-passive) is alien to me (especially the agent part).

I guess the oni-passive refers to something like "Suomessa puhutaan suomea ja ruotsia." = "One speaks / you speak...".
While the esti-passive refers to something like "Viime viikolla meidän keittiö maalattiin.", which you wouldn't translate as "one painted our kitchen" but as "our kitchen was painted".

As the passive voice removes the agent (and possibly introduces it again in the periphery), it is often used, when the agent is either unknown or of no concern. It doesn't matter, who exactly speaks Finnish or Swedish; and it doesn't matter who painted the kitchen. Hence the passive voice is a good choice.

As you have pointed out correctly, in Esperanto we can also use active verbs with "oni" as the subject and it serves most of the time the same purpose. "Oni parolas la finnan" and "la finna estas parolata" mean basically the same. This doesn't work all of the time however: "Mi estis elektrokutita" and "Oni elektrokutis min" are different. If I by accident touched a high-voltage cable then I can say (maybe to my creator or [...fill in deity of your choice...] ) "mi estis elektrokutita", but not "oni elektrokutis min", because "oni" implies some agent.

Verbs derived from transitive verbs with -iĝ- are not passive verbs. I had quite a nice and interesting conversation about this with Kirilo (if I only could search the forum for this thread), where I proposed to see -iĝ- verbs as anticausative (parallel to the causative -ig-) and he concurred that this is a valid (and not even new) interpretation.

Maybe the passive flavour of iĝ-verbs from transitive verbs is more semantic. Generally, if X-i is transitive, then X-iĝ-i means X-at-iĝ-i, with a hidden and implied passive. You applied this principle when you wrote "The verb legiĝas has the iĝi ending, ah, it becomes read". You immediately interpreted "leĝigi" correctly as "iĝi legata" (become read) and not as "iĝi lega" (become something related to reading).

Espels,

Let's take a look at your sentences.
 

• Li diris la diagnozon kaj nia lasta espero mortiĝis : OK
  Here the root, mort/, has intranstive verb-like character (first entry in the dictionary). The use is a bit old-fashioned but Zamenhofian. Using more contemporary language …espero mortis. Furthermore the sentence does not explicitly say, that the words killed the hope, albeit that is implied. This is common with iĝi verbs.
  
  
• La vesto puritiĝis bone : NOT OK
  The root pur/ has adjective-like character, so puriĝi would be an ordinary iĝi verb, to become clean (note, clean, not cleaned). While in theory you can form a verb from a passive participle (purita → puriti, puritigi or puritiĝi), that is not a good idea in many cases, because they not necessarily carry the meaning you intend and often the listeners/readers have hard time to decipher them. You translated this to "The cleaning of the clothes was easy", which should reveal that a noun ("the cleaning") would serve you better, i.e. La purigado de la vesto estis facila.
  
  
• "Ĉu vi vidas tie la grandan arbon?" iris la sorĉistino, montrante arbon, kiu troviĝis apud ili : OK
  The root trov/ has transitive verb-like character, so there is nothing extraordinary in troviĝi. I know, that it is usually translated to "to be situated/located/found" into English, but that's just how English works. English uses much more passive voice than Esperanto mainly because of the strict word order. There is no need for such complex expressions in Esperanto, keep it simple.
  
  
• La pordo malfermiĝis : OK
  Same as with troviĝi, from a transitive verb-character root.
  
  
• Ruĝiĝi de honto : OK
  Ordinary iĝi verb created from an adjective-character root.

Nornen,

You have two ways to express the same thing.
 

• La libro estas legata. (esti-passive. cf. werden-passive in German)
  
• Oni legas la libron. (oni-passive, cf. man-passive in German)

If you take the standing, that passive describes a change of the state of an object (focus on the object), then yes, in la libro is the subject (the one of which state changes). However if you take the standing, that passive impersonates the action (focus on the action), then no, la libro cannot be the subject by the definition of this kind of passive, it's an object (the one to which the action effects).

Yes, from some native languages' view oni is pseudopassive, but from some others' view esti-passive is not passive at all. In order not to stuck at that, I've chosen to call them both passive.

Yes, I'm aware, that the oni-passive is limited to cases, where the agent must be thought to be one or more unspecified persons. Therefore one indeed says Mi estis elektrokutita instead of Oni elektrokutis min. On the other hand the esti-passive requires, that the corresponding verb in the active voice has a direct object. You can't say En la parko estis kurita, but you say Oni kuris en la parko. So both are needed, but I recommend the oni-passive whenever possible, because it is much simpler.

I can see, why some perceive iĝi verbs to have a passive voice character, but to my understanding I have never claimed, that they would be in passive. I think, that those who claim so have a faulty logic. I base my standing on the following. Since the basic meaning of verbs with the iĝi ending is "to become…", and this applies to noun- and adjective-character roots (tagiĝi, puriĝi). By the same logic legiĝi means "to become to read"/iĝi legi. Note, not "to become having been read"/iĝi legita. But iĝi legi is nonsense, and by saying, that legiĝi means iĝi legita, you're creating an exception. Esperanto is no exception, it has exceptions, but creating them on purpose is not the way to go.

When it comes to comparing igi and iĝi, I have been taught from the very beginning, that igi means "to make…" and iĝi "to become…".

Metsis:Espels,

Let's take a look at your sentences.
 

• Li diris la diagnozon kaj nia lasta espero mortiĝis : OK
  Here the root, mort/, has intranstive verb-like character (first entry in the dictionary). The use is a bit old-fashioned but Zamenhofian. Using more contemporary language …espero mortis. Furthermore the sentence does not explicitly say, that the words killed the hope, albeit that is implied. This is common with iĝi verbs.
  
  
• La vesto puritiĝis bone : NOT OK
  The root pur/ has adjective-like character, so puriĝi would be an ordinary iĝi verb, to become clean (note, clean, not cleaned). While in theory you can form a verb from a passive participle (purita → puriti, puritigi or puritiĝi), that is not a good idea in many cases, because they not necessarily carry the meaning you intend and often the listeners/readers have hard time to decipher them. You translated this to "The cleaning of the clothes was easy", which should reveal that a noun ("the cleaning") would serve you better, i.e. La purigado de la vesto estis facila.
  
  
• "Ĉu vi vidas tie la grandan arbon?" iris la sorĉistino, montrante arbon, kiu troviĝis apud ili : OK
  The root trov/ has transitive verb-like character, so there is nothing extraordinary in troviĝi. I know, that it is usually translated to "to be situated/located/found" into English, but that's just how English works. English uses much more passive voice than Esperanto mainly because of the strict word order. There is no need for such complex expressions in Esperanto, keep it simple.
  
  
• La pordo malfermiĝis : OK
  Same as with troviĝi, from a transitive verb-character root.
  
  
• Ruĝiĝi de honto : OK
  Ordinary iĝi verb created from an adjective-character root.

According to grama rules from here (lernu):
An IĜ verb made from an intransitive verb shows transition to the action in question. IĜ with that sort of verb is therefore almost equivalent to the prefix EK.
Mortigxis = ekmortis.
Our hope began to die.
Also:
IĜ-verboj montras la nuancon, ke la ago okazas per si mem, aŭ ke la ago okazas senvole:
"Mia onklo ne mortis per natura morto, unu tagon, promenante apud la reloj de fervojo, li falis sub la radojn de veturanta vagonaro kaj mortiĝis". My uncle died by accident.
Jam simpla morti montras transiron (de vivo al morto). Ĉi tie IĜ montras, ke la morto okazis senvole, akcidente.
And other from a dictionary:
Sxi drinkmortogxis.
La patro enfalis el fenestro de tria etagxo kaj mortigxis.
If the "La vesto puritigxis bone" is not good for you, here the another one:
La tagoj longiĝas, printempo alvenas. This sentence from lernu, and have the same structure: adj. root + igx.
These two from a dictionary:
En la kota vetero mia vesto forte malpurigxis
En ilia busxo la sankta vorto "amo" malpurigxas.

Espels,

It boils down, what character the root has.

• longiĝi ← longa : long/ has adjective-like character, therefore the iĝi verb is an ordinary iĝi verb.
  
• mortiĝi ← morti : mort/ has intransitive verb-like character. Yes, the iĝi form has a nuance of being senvole, akcidente, but such a use is considered somewhat old-fashioned nowadays. Subite/akcidente mortis expresses the same idea in a more simpler way.

The problem with puritiĝis is, that it combines the passive participle, -it-, with the iĝi ending that is in active. I.e. pura : clean → purita : having been cleaned → puritiĝi : to become by itself having been cleaned, eh???? The word is too complex and it's not even clear, what it means, so try to express the idea with simpler expression, possible using additional words.

PMEG has a chapter about iĝi verbs, but reading and understanding of PMEG is not necessarily trivial.

Finally, English is notorious for lacking mark-up, it relies on word order and context. For instance the word "cleaning" can be understood as a noun or a verb or…

Metsis:Espels,

It boils down, what character the root has.

• longiĝi ← longa : long/ has adjective-like character, therefore the iĝi verb is an ordinary iĝi verb.
  
• mortiĝi ← morti : mort/ has intransitive verb-like character. Yes, the iĝi form has a nuance of being senvole, akcidente, but such a use is considered somewhat old-fashioned nowadays. Subite/akcidente mortis expresses the same idea in a more simpler way.

The problem with puritiĝis is, that it combines the passive participle, -it-, with the iĝi ending that is in active. I.e. pura : clean → purita : having been cleaned → puritiĝi : to become by itself having been cleaned, eh???? The word is too complex and it's not even clear, what it means, so try to express the idea with simpler expression, possible using additional words.

PMEG has a chapter about iĝi verbs, but reading and understanding of PMEG is not necessarily trivial.

Finally, English is notorious for lacking mark-up, it relies on word order and context. For instance the word "cleaning" can be understood as a noun or a verb or…

Of couse it should be "La vesto purigxas bone", without -it. It was a mistake. Niether Esperanto, nor English is my first language.
Anyway "purigxi" and "mortigxi" can exist but you recently said they can't.

Espels:
Of couse it should be "La vesto purigxas bone", without -it. It was a mistake. Niether Esperanto, nor English is my first language.
Anyway "purigxi" and "mortigxi" can exist but you recently said they can't.

Ah, that typo threw me off. Namely there are speakers, who make verbs from participles.

I've said, that mortiĝi (iĝi verb from a intransitive verb) is old-fashioned. Normal morti covers most cases, and if you really to emphasize suddenness, use subite, akcidente or something similar. The chapter of iĝ verbs in PMEG gives further possibilities to express nuances for verbs in this category.

Generally speaking of iĝi verb based on intransitive verb-character roots, In the same chapter PMEG says:

PMEG:
Se verbo estas senobjekta, kaj se ĝi per si mem montras transiron al nova stato, aldono de IĜ normale estas sensenca kaj eĉ erara.

Some books simplify things and say forms like puriĝi and mortiĝi are wrong. They are not wrong, but they are very seldom needed.

PS. English is not my native language either.