Ordinarily, when one's body is killed, the soul departs for the next world. If, however, the body of a horcrux owner is killed, that portion of his soul which had remained in his body will not pass on to the next world, but will rather exist in a non-corporeal form capable of being resurrected by another wizard. If all of someone's horcruxes are destroyed, then his soul's only anchor in the material world would be his body, the destruction of which would then cause his final death. To destroy the horcrux, the destroyer must destroy it in such a way that it is put beyond magical repair. In the seventh book, Gryffindor’s sword, which is impregnated with Basilisk venom, Basilisk fang and Fiendfyre are the substances used to destroy them.