harry potter - Could Voldemort have won the Elder Wand through his Horcruxes?

In Harry Potter and the Half Blood Prince:

The original plan is for Snape to kill Dumbledore, but before he can, Draco Malfoy disarms Dumbledore, which (even though he doesn't know it), transfers control of the Elder Wand to Draco before Snape can kill Dumbledore.

This becomes an issue later, in Harry Potter and the Deathly Hallows:

Voldemort knows he doesn't have control of the Elder Wand and thinks it is Snape's, so he kills Snape to win the Wand's obedience, but this doesn't work because Snape was never the Wand's master.

We know that what took place in Half Blood Prince was planned out by Dumbledore because:

Dumbledore would die within a year, in a painful way, due to the trap he was caught in when he was searching for Voldemort's horcruxes.

Which leads me to wonder:

If Dumbledore had not been disarmed or killed in Half Blood Prince, and he died as a result of the trap set for him, would Voldemort have won the Elder Wand? There was no duel, no direct contest, and no use of wands to combat each other, just a sneak trap left behind to protect the horcrux.

So would a trap or something similar that kills a person still be enough to win the Elder Wand, or does it have to be won through the use of wands or some type of actual combat?

Answer

This is such an interesting question!

I think it would be possible to master the Elder Wand through accident or trap. In Tales of Beedle the Bard it says:

Believers in the Elder Wand, however, hold that because of the way in which it has always passed allegiance between owners – the next master overcoming the first, usually by killing him – the Elder Wand has never been destroyed or buried, but has survived to accumulate wisdom, strength and power far beyond the ordinary.

Godelot is known to have perished in his own cellar, where he was locked by his mad son, Hereward. We must assume that Hereward took his father’s wand, or the latter would have been able to escape, but what Hereward did with the wand after that we cannot be sure.

Tales of Beedle the Bard - Page 103 - Bloomsbury Edition

As Harry demonstrated with Draco, disarming does not have to involve either Expelliarmus or Avada Kedavra. So it's conceivable that a trap laid that resulted in a witch or wizard losing their wand, and that wand being taken up by a new wizard, would qualify as mastering the former's wand. It's also dependent on the wand; Ollivander explains that usually a wand will bend its will to a new master, but not always. Based on Godelot's predicament, I think your idea is quite possible.