It depends how it was brought there. Their are generally two ways to get Outsides to Prime. Summoning or Calling, although plane travel magic is also possible. A Summoned (see the sub-school attached to the conjuration spells like Summon Monster) creature vanishes and reforms/returns to its home plane. Called creatures are brought permanently to the plain and when killed die dead. An Outsider that plane travels is under the same problem as a Called creature, it will die if killed.
A quick way for a non-native Outsider to get out of a bad situation is to get themselves banished back to their home plane.
Dismissal is a Cleric 4 or Wiz/Sorc 5 as apposed to Plane Shift at Cleric 5 or Wiz/Sorc 7. This for those cases where another spell or effect can't get them out of trouble.
There is also a decent amount of flavor in most settings on Outsiders that their core essence is never permanently destroyed. For a lack of better work they eventually "reincarnate" in a nearly identical form. This is often described as having limited memories of their past life but they are a different entity and may have a different personality (within the limits of Outsider race).
The PF Chronicler still lists their main abilty as
PRD
Bardic
Music (Su): At 3rd level, a Pathfinder chronicler gains this ability, which functions like the bard class feature of the
same name, except that the chronicler's effective bard level is 2 lower than her class level. Levels in this class stack with levels in any other class that grants a similar ability to determine her effective bard level.
That was changed to Bardic Performance on the bard, a minor issue unless your hard core RAW eater. As there technically isn't an ability called "Bardic Music" anymore, so it adds to nothing (very very hard core RAW).
Additionally
(Greater) Epic Tales,
Whispering Campaign(odd point here), and
Inspire Action all still use the Use per Day mechanic of Bardic Music and not the rewritten Bardic Performance. To odd point Whispering Campaign also doesn't mention how many daily uses it consumes for its various options, so one would be inclined to assume 1 day for type.
If you convert it directly as is you get some very strange and likely unknown problems
(like a great deal of problems that the change in Bardic Music/Performance brought with it, and should have been mass tested before hand). For most is Inspire Action which lets you grant an ally a Move Action(later a Standard Action) for 1 Round of Rounds/Day (or 1 Daily use interoperated literally). Granted that's going really out a limb for rules interoperation but that's the mess they left when they missed the PF Chronicler in their sudden change in the Bard rules. It makes the PF Chronicler virtually useless and broken (in both senses) out of the box.
