Here's what actually happens:
* Voldemort believes Draco disarmed Dumbledore: In the Half-Blood Prince, Draco attempts to kill Dumbledore but fails, and Dumbledore ends up dying from Snape's curse. Voldemort believes Draco disarmed Dumbledore, making him the new owner of the Elder Wand.
* Voldemort seeks Draco's allegiance: Voldemort seeks Draco's allegiance, thinking he now possesses the Elder Wand's power. Draco, however, is terrified and does not actually believe he owns the wand.
* Harry disarms Draco: In the Deathly Hallows, Harry disarms Draco during the Battle of Hogwarts. This action unknowingly makes Harry the new owner of the Elder Wand, as the wand's allegiance shifts to the disarmer.
* The Elder Wand's true owner: Harry later discovers the true owner of the Elder Wand is not Draco but actually Neville Longbottom, who disarmed Voldemort earlier in the book. However, Neville was not aware of the Elder Wand's power and its significance.
It's a common misunderstanding that Draco obtains the Elder Wand, but it's important to remember that the wand's allegiance is based on the act of disarming its previous owner.