You have a horcrux. Then a dementor comes along, and, I don't know why but it does, 'kiss' the horcrux. What do you think happens?

Remember Hermione said "A Horcrux is the complete opposite of a human being. If I picked up a sword right now, and ran you through with it, I wouldn't damage your soul at all. My point is that whatever happens to your body, your soul will survive, untouched,” said Hermione. “But it’s the other way round with a Horcrux. The fragment of soul inside it depends on its container, its enchanted body, for survival. It can’t exist without it.”

Does a dementor kissing a horcrux destroy it???