Harry left "a portion of his life" (not an exact quote) in Azkaban, and apparently it will remain there forever. That could be the remnant that Death would fail to destroy.

Anyway, Snape drew attention to the final line in the prophecy. It talked about two different spirits that couldn't exist in the same world, or perhaps two ingredients that cannot exist in the same cauldron. That's not Harry and Voldemort; that's Harry and Death.

I mean, Harry has already sworn to put an end to death. It's how he casts his patronus. He's a lot less sure about killing Voldemort, and would prefer not to, if given the choice.