Answer:
The Phantom does not die. In all versions Meg Giry finds his mask on his throne; in some that is the final scene, in others she also finds his cape; in Webber's movie adaptation it is shown that many years later, when Raoul is old and Christine has died that he still lives.
The Phantom does not die in Webber's musical, but he does die in the original book by Gaston Leroux. In the book Erik dies of a broken heart.