This answer to a different question (about D&D 5e) says:
To open, lets look at a sample of the rules that say you cannot permanently kill such a creature outside of their home plane...
The only way to truly destroy a demon is to seek it in the Abyss and kill it there.
Devils that die in the Nine Hells are destroyed forever
Only on its native plane can a yugoloth be destroyed permanently
Of note: Angels in the 5E MM do NOT have this protection. Weird as it may seem, it is actually easier to kill a Celestial than it is to kill a Fiend.
So, going by the lore available in 5e, it is implied (only by the lack of any details to the contrary) that celestials can be killed permanently on any plane. Obviously this quote doesn't mention fey, but I think of celestial, fiends and fey as being grouped together due to certain spells in 5e, such as find familiar or find steed, saying that the spirit can be one of those three.
Anyway, my question is, even though the lore stating that fiends (specifically devils, demons and yugoloths) cannot be killed outside their native planes is well established, is there any lore from any edition of D&D that suggests that the same rules exist for celestials or fey (such as angels or satyr, for example)?