This would certainly be a very risky way to destroy a <PERSON>. For one thing, I don't think that anyone's going to be able to fool a dementor into Kissing an inanimate object, like the other <PERSON>, (<PERSON> made a good point there) so this is probably only something that could be used on animals, magical creatures, and humans. There is, of course, the fact that you can't really control a dementor...but fiendfyre is cited as a way to destroy Horcruxes, and <PERSON> says that she would never have suggested they use it because of how difficult it is to control--we see how well that worked for <PERSON>. You'd have to be able to speak Parseltongue to control a Basilisk, and I guess there really isn't a way you could "harness" the ability of a dementor to suck out a soul the way they are able to use to detatched Basilisk fangs.
Then there is the question as to whether or not the soul of the carrier who has been made into a Horcrux, like <PERSON>, would lose their soul or that of the Horcrux. I would say that <PERSON>'s soul and <PERSON>'s soul fragments are separate, not merged, because <PERSON> says that part of <PERSON>'s sould "latched itself on to" <PERSON>...now, would <PERSON>'s sould or <PERSON>'s go first? That's where there's really the risk...does <PERSON> have a "primary" soul and then a "secondary one"? Maybe since <PERSON>'s soul latched onto his own, it's sort of like that one is "on the exterior" in a manner of speaking, and it would be destroyed first, being why <PERSON> was able to remove the Horcrux part of <PERSON> without killing and damaging <PERSON> and his soul. But, this could have only been because it was <PERSON> killing <PERSON> and <PERSON> sacrificing himself. 773
Then again, <PERSON> shouldn't destroy your soul at all, so that must have been a special circumstance. Which leads us to what's unique about the dementor's Kiss.
I would have to go with what <PERSON> says, asserting that the dementor's Kiss destroys a soul, and it is then lost forever. This sounds pretty much like what you want to happen when you destroy a Horcrux. The dementor doesn't release the soul so it's floating around somewhere, it completely gets rid of it. So that means that the dementor's Kiss should, in theory, be able to destroy a Horcrux. The risk is whether or not the dementor would destroy a living Horcrux before the soul of that living thing, and then, anyway, there's nothing to stop the dementor from going on to suck out the second soul, too. 773