"Everyone must die."
Translation:Ĉiu devas morti.
When -iĝ- is added to a verb, it essentially removes one of the actors. So "fandi" means "to melt something. Adding -iĝ- (fandĝi) removes the melter and leave the meltee (it means that something melts). "Morti" only has one actor, so mortiĝi would be a verb with no actors, which is nonsense. One could argue that it means "fariĝi morta" but that's already what "morti" means. In other words, don't say "mortiĝi".
Edit: [One year later] Analogous to sidi/sidiĝi, the word mortiĝi could be contrived to mean "become dead" - however, it's not a word I use and PIV has it marked as a word to be avoided.
This is an inadequate explanation of the effect of the suffix -igx- on argument structure in Esperanto, partly because it ignores the fact that roots are not parts of speech, and partly because the suffix doesn't really directly affect argument structure. What it does affect is semantic structure. "Rugx-" is a root that has to do with redness. As a verb "rugxi" means "to be red." Adding the suffix "-igx-" to it yields a verb that means "to become red." That doesn't remove any actors (unless you want to point out that in the case of being red, nobody was acting to begin with). Unfortunately Zamenhof was not as clever as he thought he was, and Esperanto is much more idiosyncratic and irregular than anyone wants to admit. The verb "morti" ought to mean "to BE dead" (then the sentences "li mortas" and "li estas morta" would mean the same thing, similarly to "li rugxas" and "li estas rugxa") and then the verb for dying would be, quite sensibly "mortigxi." As it is, "mortigxi" ought to be either just a synonym of "morti" (cf. English "use" and "usage") or possibly an inchoative of it, with a meaning along the lines of "to start dying."
Sorry to be inadequate. It's difficult to cover every nuance in five lines and get the kids to all their activities on time. It is, however, generally accepted among Esperanto grammar theorists that roots really do have a grammatical quality. This follows naturally from the meaning of the root. So, when I said previously that "mort-" is a verb, what I really meant was that "mort-" is a root with a verb-like quality, based on the meaning of "mort-".
What is idiosyncratic is not the meaning of "morti" but rather the meaning of "morta", which according to some patterns in the language should mean "pertaining to dying" and not "dead" as it actually means.
I would also argue that this is another reason to save expressions like "rugxas" for special cases, because it's best to look at it this way: "gxi estas rugxa" and "gxi rugxas" do NOT mean the same thing. That's why there are two ways to say it.