What happens when a person, monster, animal etc is possessed but dies? Such as a PC kills the possessed creature, a suicide, or any other means? What happens to the creature causing the possession? Does it die as well or is just sent from the body?
Having been in a scenario where I was possessed by a ghost and then it killed itself I can tell you from experience: the possessed dies and possessor (eg the ghost) survives. If I remember right this was in The Forge of Fury.
Additional info assuming D&D 3.5, based on a ghost from the d20 SRD:
Once per round, an ethereal ghost can merge its body with a creature on the Material Plane. This ability is similar to a magic jar spell (caster level 10th or the ghost’s Hit Dice, whichever is higher), except that it does not require a receptacle. To use this ability, the ghost must be manifested and it must try move into the target’s space; moving into the target’s space to use the malevolence ability does not provoke attacks of opportunity. The target can resist the attack with a successful Will save (DC 15 + ghost’s Cha modifier). A creature that successfully saves is immune to that same ghost’s malevolence for 24 hours, and the ghost cannot enter the target’s space. If the save fails, the ghost vanishes into the target’s body.
This leads us to the Magic Jar spell:
If the host body is slain, you return to the magic jar, if within range, and the life force of the host departs (it is dead). If the host body is slain beyond the range of the spell, both you and the host die. Any life force with nowhere to go is treated as slain.
Although mirvl20 has given the canon answer (which is rather good +1), I think you could also have some fun with it too. These are all soft things that would add to the canon of your setting, so be careful which you pick.
Perhaps the possessor is OK but has to live the effects of being inside the consciousness of something dying. That might well lead to a stress disorder. Or nightmares. Or a change of career. Or a slide in insanity.
Trapped in a ghost
Maybe the possessed walks as a ghost and the possessor is now trapped in a ghost, suffering their torment until freed. The ghost won't pass without the possessor being freed.
A little bit of me died
The possessor might lose a little piece of their personality with it, such as their nerve or perhaps sense of humour.
Perhaps the consciousness of the possessed is part of the possessor now, giving them multiple personality disorder. Can be used for frightening effect if the two personalities are opposing. Can be used for fun if the possessor was possessing a sheep to spy on an enemy. Think about what the trigger might be to switch personality.