What would happen to the Elder Wand if a living Horcrux killed its current wielder?

Question

What happens if a Horcrux (or indeed, any other non-wizard being containing part of a wizard's soul) kills the owner of the Elder Wand?

For example, consider when Dumbledore was still the master of the Elder Wand; suppose Nagini had killed him.
Nagini is not a wizard; since only wizards can wield a wand, it would seem like the Elder wand should remain with Dumbledore forever.
On the other hand, Nagini, as a Horcrux, has a part of Voldemort's soul inside it. Would that be enough for the Elder Wand to change hands?

Answer 1

It would count as Voldemort performing the deed.

We have canonical evidence for this: Nagini was the one who killed Snape, which would have enabled mastership of the Elder Wand to pass to Voldemort (assuming Voldemort had calculated the consequences of his deed correctly, which we should probably assume he had).

Nagini killed Snape on Voldemort's command, but if Voldemort had commanded a Death Eater to perform the deed, then the Death Eater and not Voldemort would have become the master of the Elder Wand. We see this with Draco Malfoy: Voldemort ordered him to kill Dumbledore, but when he Disarmed Dumbledore, the Elder Wand mastership passed to him and not Voldemort.

Nagini is a Horcrux of Voldemort, containing part of his soul. If she had killed Dumbledore, then mastership of the Elder Wand would have passed to the owner of the piece of human soul inside her, i.e. to Voldemort.

See also this answer.

Answer 2

I don't think it would count as Voldemort - after all, Harry was also a horcrux, at the time he won allegiance through Malfoy. Of course, Nagini is acting within Voldie's will, and Harry as his own person, so that might complicate it... but I think the answer is no.

As for what would happen to the wand's allegiance? Harry wins the wand through a duel with Malfoy which happened without the elder wand being present (or even known to be relevant). So it might be the wand will go 'looking' for a wielder among those who last disarmed its previous owner, even if it was a different wand being won at the time. There would almost have to be some mechanism for reuniting the wand and the mastery of the wand, or restarting the claim of ownership, if its allegiance can separate from the wand itself to pass through the second hand defeat of those who might not even know they've won it.