Voldemort has said that it was his desire “to conquer death,” a classic mark of a dark lord. He sought this with his attempt to gain the Sorcerer’s (Philosopher’s) stone created by the alchemist, Nicholas Flamel, but failed, due to the efforts of Harry, and his best friends, Ron and Hermione. If Voldemort achieves immortality, he would no longer have to worry about Harry Potter, who he will outlive, and with Harry’s death, the prophecy may be fulfilled.

On the other hand, we may argue that the prophecy would not be fulfilled with the natural death of Harry, in relation to an immortal Voldemort. It does state that there is a boy who would have the power to vanquish (destroy, kill) Voldemort, or vice-versa. Logically, we cannot say that Voldemort had "vanquished" Harry, if Harry had died naturally. The prophecy seems to point out more towards an outright "outdoing" of each other, till one is dead and the other alive.

Yet, even if Harry attempts to kill an immortal Voldemort, it would not be possible because it is fallacious to end the life of an immortal, unless there was “one way” to kill an immortal, a la Highlander, by cutting off the head (then what is the point of immortality?). But this is Rowling’s magical world, not Duncan McCloud’s. Until then, or until he finds some other way to achieve immortality, he would still have to uphold the prophecy, as a mortal who is still subject to being thwarted for good by Harry Potter.