It's a question that has never been directly answered by J.K. Rowling, and one that we could talk about for days but never necessarily solve.
That said, we would like to have a discussion on this question anyway because it came up on the newest episode of Alohomora! - which has yet to be released - and it's often fun to ponder these wild questions.
We know from the canon that a Dementor's Kiss is the ultimate form of punishment, in which a Dementor clamps its jaws on a victim's mouth, leaving him or her in a vegetative state by sucking out the victim's soul.
But our question today is this - what exactly happens to this soul when it's sucked out? Is it instantly destroyed? Is the victim's soul doomed to a kind of Dementor purgatory where it continues to exist? Does the Dementor absorb that soul and with it the personality of the victim...therefore in some way becoming the victim?
That latter possibility is a bit crazy, but what do you think? Some answers to this question will be read on the next episode of Alohomora!