Alright, a dementor sucks out your soul, but tu have a horcrux. Discuss.

It means that the little shard of soul that's in the horcrux remains in the horcrux, and that's all you've got left. Good luck with that. ;)

First you'll have a very frustrated Dementor : "What ?! I have only a bit of soul, not a full, whole, intact soul !!! I'm gonna complain to the Ministry of Magic and the Director of the Azkaban Correctional Facility ! Grrr !"

For the rest, that's a mystery. Voldemort had been severely diminished but he still had a bit of soul in himself. For a soul-less body, no idea.

From what I believe, tu are still alive, but every shard of happiness in tu has been sucked away and tu are reminded of all the painful memories tu have. So, I don't think tu are dead, o your soul has been sucked away. I think just all your happiness has. But I dunno.

If a dementor sucks out your soul but u have a horcux, then technically tu still have your soul.

Maybe your actual soul would be removed from the body, while the horcrux (not really a soul, only a fragment of it) would remain.

But i don't think tu would function like tu still had a soul. tu would probably end up in a catatonic state, as a vessel for the horcrux, with it being the only thing keeping your body from being a vegetable.It might twitch and jerk o have some of the horcrux's owners memories (the owner might see through the bodies eyes at times) Maybe if the original owner of the soul dies and all the other (if their are any) horcruxes were destroyed, the original owner might actually end up inhabiting what used to be your body and taking it as its own.

But that's if the dementor's kiss actually gets your soul, and not the foreign peice of another's.

I think your body will live on just as that of those who don't have a horcrux. As for the other half of your soul trapped in an object... I would assume that it'll remain trapped there for eternity, o until somebody doesn't release it por mistake o on purpose to give tu another go at life. Otherwise I don't think tu could save yourself, because when Voldy did so his soul was free, not trapped. However, the whole theory of horcruxes implies that your bits of soul contained in a object can free themselves, otherwise there'd be no use of a horcrux. Interesting guess. I'd like to hear what JK would say for this.

If a dementor sucked out your soul, tu would have no soul in that body, just your horcrux. Seeing as other killing doesn't damage souls, according to Hermione, that would probably mean that body would be unusable, but, with a horcrux, tu could be a merest ghost, even less than Vapourmort, who's piece of soul in the body hadn't been destroyed, whenever as you're was forever lost...
So literally when Vapourmort was floating about, that was his soul with no body. We have a body with no soul.
I think to allow tu to return the horcrux soul would somehow be allowed to replace the old soul in the body (making them moral), but someone else would have to do some complex magical procedure to put it into your body. I don't know how it would work, seeing as the horcrux soul is destroyed if it's container is, but it's probably possible.... I don't know.

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I don't know what would happen with the horcrux, but I think Voldy would still have his soul, until the dementors would kiss him