Outsiders and Afterlife.

[Braininthejar]

I know the most basic rule - "a summoned creature goes back home when killed, a called creature dies when killed."

But are there any other rules for outsiders dying?

I remember in D&D some fiends would eventually come back, unless killed on their home plane. Is anything like this in effect in Pathfinder?

I know demon lords are on a 1 year respawn timer. Anyone else has special rules for dying permanently?

[Mysterious Stranger]

There are two subschools that can summon a creature from another plane. The calling subschool brings the real creature to the plane it is summoned on. If the called creature is killed it actually dies unless it has an ability that brings it back. The summoning subschool is the one that the creature does not die if killed. A summoned creature is sent back when it is killed, or its HP drop below zero.

That means outsiders that are not summoned die just like any other creature.

[Diego Rossi]

The "outsiders respawn when they are killed, possibly weaker, unless you do it the right way" trope isn't present in Pathfinder.
Some specific creature can return after it has been killed, but it usually works for that specific creature, not a whole type.

Fey killed in the First World return after a time, generally changed, but that is mostly a feature of the First World, not of the fey. It can happen to non-fey creatures that have lived in the First World for a long time, too.

High-level mythic characters can return, some named demon or devil lords can return (it is in their specific stats), and so on, but there is no generic rule for a type.

[I grok do u]

Core rule relates to have to bring back to life:

Outsider traits wrote:

Unlike most living creatures, an outsider does not have a dual nature—its soul and body form one unit. When an outsider is slain, no soul is set loose. Spells that restore souls to their bodies, such as raise dead, reincarnate, and resurrection, don’t work on an outsider. It takes a different magical effect, such as limited wish, wish, miracle, or true resurrection to restore it to life. An outsider with the native subtype can be raised, reincarnated, or resurrected just as other living creatures can be.

Fortunately, the AoN bestiary gives background information/fluff on the various outsider subtypes. This can be used to decide any storyline fates. For example:

Monad, the Condition of All (Aeon) wrote:

All aeons are bound in a state they know as “the condition of all” or “monad,” a supreme oneness with all members of their race and the multiverse itself. Therefore, aeons exist as an extension of the multiverse; in a fashion similar to the way bones, muscle, and the various humors create a mortal, they exist as part of a greater being. When destroyed or upon accomplishing specific goals, their energies simply dissipate and become reabsorbed into the monad. They do not die, but are instead recycled. They have no discernible memories and seem to exist only in the present, arriving to repair balance. Relationships with non-aeons are generally nonexistent, and they feel no sense of affection, remorse, vengeance, or similar emotions. Aeons deal with each task as its own action, independent from all other tasks. Thus, an individual once at violent odds with an aeon may, upon their next encounter, have the aeon's full and undaunted support.