He was in possession of the deathly hallows because the wand was his the cloak was his and then the stone was his. That is why he did not die. He cast a spell on Harry, intending to kill him but instead killed the seventh horcrux, which was the last part of his soul so Voldemort dies before he can actually kill Harry.
Source: Warner Bros. Another reason for Harry ultimately dropping the stone is that if he were to get rid of it, then that would mean no one else could become a Master of Death. This means that Voldemort would never be able to simultaneously possess all three of the Hallows.