that post about the resurrection stone got me thinkin. it's established in Canon that there IS an souls/ Afterlife. and it seems obvious James/Lily, the others,etc souls went there. but then what Were the spirits/souls that came out of Voldemorts wand in GoF? were the souls trapped there? and also if the resurrection stone intent is for people who use to die, were the 'loved ones' call back their real selves? this really puzzles me.
For Harry, his connection to his “resurrected” loved ones ends when he dies, so it’d probably be the same for anyone else. I always imagined it was something like their souls being called back by the events that occurred. When the resurrection stone came into effect, I assume “the platform” (that is to say, the barrier between worlds) was open for Lily and James, and they were able to travel between worlds, but they were without truly substantial bodies and thus unable to truly come back to life. You can interpret the prior incantatem seem as much the same thing, or as simply the magical impression left by the killing curse. The true effect of Avada Kedavra is never delved into beyond the fact that it kills people. Perhaps the reason Harry’s parents, among others, appeared from the connected wands is that when the killing curse ends your life, it takes a part of you. And that something is seen in priori incantatem.