I'm A Banana
Potassium-Rich
I, as DM, own them.
Before they play them, as they play them, after they play them! They are mine, all MINE!!!! MWAHAHAHAHA!!!
I like putting former PC's in embarrassing outfits, making them beg on city streets, ensuring that they had a messy breakup with their love interests, giving them horrible scars and at least three infectious diseases that are highly visible and involve various kinds of pungent oozing. If their former player's new PC encounters them I have the former PC cry a little bit and soil themselves in confusion. All of their magic items were eaten by roving disenchanters, and their priests have asked them to never set foot in their temples again.

Honestly, this has never come up in my years of D&D. As both a player and a DM, each campaign is pretty self-contained, and the only way I stop playing a PC is usually because they've seen themselves out of the main action for some reason (retired, gone mad, died), so either my former PC's are either literally in another universe, or at least functionally are. I suppose I imagine them pretty much in the DM's hands, and though it'd be nice if the DM considered my hopes and dreams for the character, I don't mind too much if they didn't.