What exactly happens to the essence of a petitioner that dies off their home plane? Does it just dissipate into nothingness? Does it dissipate into Astral, or merge with whatever plane they find themselves on? I know in some specific circumstances, it merges back with their god, but I don't recall what happens to a regular petitioner though (if there even was anything ever written about it).
When petitioners die off-plane
I've always thought that the petitioner became one with that plane, as well. On its home plane, this was a comfortable merging, because most of the petitioner's spirit was compatible with that plane's alignment and attitudes, and so the petitioner survives in some eternal abstract form as part of the plane's strength. When it happens naturally, it's because existence in the plane has slowly refined all aspects of the petitioner's spirit to the point where there are no noncompatible features remaining, and the lines between it and the plane just vanish. Imagine the petitioner as a lamp that has been tuning its color; once it perfectly matches the light all around, you can't see it anymore, but it's still strengthening the light you see. When the petitioner dies by violence on his home plane, most of himself survives; the few remaining incompatible bits react interferentially with the plane, and for all practical purposes cease to exist along with the tiniest portion of the plane's strength.
When the petitioner dies off-plane, most of his personality doesn't match the plane, so as it merges most of it fights the plane and sets up such an interference, cancelling out some of the local energies. Only those parts of himself that match the local plane, imperfect parts he would rather have been rid of in the first place, survive and merge with the local plane. What's eternally left of him are the parts he doesn't like anyway. A dreadful fate, unless he's particularly militantly-minded: a squadron of dwarven einheriar marching from Arcadia to Acheron might consider their sacrifice worth it to weaken Acheron's evil (though we, secretly, know their gods save them from such a fate).
Page 33 of On Hallowed Ground:
'... a petitioner killed while away from his home plane is dead, gone, lost forever.'
And then it talks about a few exceptions - but in general, yeah, gone.
I've always thought that its a matter of belief like everything else in the Planes. So depending on the strength of his beliefs a petitioner could even survive or maybe his god would intervene in the process and save him.
It would be wise to treat canon(2e)material like the most common beliefs of the planes(it is after all assumed that they are written by some cutter or another but they are not all bloods) and not like a rule that you cannot do anything about.
So yes the most common belief is that the petitioner is lost forever when killed outside his plane but the Planes are infinite and anything could happen.Planescape is more than anything else a world of mysteries.
As far as I know, the normal petitioner ceases to exist altogether when dieing off-plane.
"La la la, I'm a girl, I'm a pretty little girl!"
--Bel the Pit Fiend, Lord of the First (in a quiet hour of privacy)