If a non-summoned outsider has the spell Planar Bubble (Spell Compendium, p.158) cast upon it and is then killed while otherwise not on its native plane, will it be permanently slain? Likewise, if an outsider is physically present on its native plane but in the area of a non-native's planar bubble effect when said outsider is killed, would it avoid permanent death?
The 7th-level Sor/Wiz spell planar bubble [trans] (Spell Compendium 158) says that it
creates an area around the subject creature that emulates its native planar environment. Thus, a character hailing from the Material Plane would have normal gravity, temperature, magic, and so on. This spell cast on a native of the Plane of Shadow… would make the area around the creature mimic its home plane’s normal gravity, a mild neutral alignment, enhanced shadow spells, and impeded light or fire spells. (Emphasis mine and link added.)
Emulates is different from becomes. The planar bubble spell does not, for example, surround the subject with a transported section of the subject's home plane. Instead, the spell creates an area around the subject that possesses the planar traits of the subject's home plane. Being in an area that shares the same planar traits as one's home area just isn't the same thing as actually being on one's home plane.
The planar bubble spell's effect may make the subject more comfortable, give the subject an edge in combat, or make melee combat against the subject challenging or uncomfortable for the subject's friends or foes. However, the spell's effect typically shouldn't change any creature's normal dying process. Unless the creature's dying process says so or the subject's home plane has some highly unusual planar traits, typically creatures die normally in an area affected by the planar bubble spell.
Most nonsummoned outsiders die normally no matter where they are killed
A living creature like an outsider that reaches −10 hp typically dies. However, a summoned creature doesn't. Instead, a "summoned creature… goes away if it is killed or if its hit points drop to 0 or lower. It is not really dead. It takes 24 hours for the creature to reform, during which time it can’t be summoned again" (Player's Handbook 173)
So, for example, using the core rules, it usually doesn't matter if the killer is on the creature's home plane or not when the killer slays an actual-and-for-real, totally-not-summoned astral deva, bralani, or formian queen (Monster Manual 11, 93—4, and 110 and 111, respectively). That creature will die normally and remain dead forever unless special means are employed to bring it back from the dead.
Some outsiders do have lore associated with them that sees something special happen to them when they are slain on their home planes. Fiendish Codex I, for instance, says that demons that die in the Abyss are forever destroyed (9—10).1 However, Fiendish Codex I isn't a setting specific supplement, so how that idea works—or if it's even a thing at all—will depend upon how much of Codex I's lore the DM opts to include in the setting.
Thus ask the DM before assuming that nonsummoned outsiders in that campaign can only be forever slain when they're on their home planes. Whether or not they can may differ from setting to setting, from DM to DM, and especially from edition to edition. Offing for eternity an angry angel, whirlwind dude, insect blob, or demon lord may be easier or harder than initially expected.
1 To be clear, the planar bubble spell still isn't a factor here: making an area so it's like the Abyss doesn't make the area the Abyss.