What happens when it evaporates, the singularity of a black hole?

Not so easy to imagine, given the diversity of the forms taken by matter in the Universe, over millions of years, there was only neutral gas atoms of hydrogen and helium. And similarly, it is difficult to imagine that one day, in a million billion years all the stars will be darkened. There will be only the remains of our still alive… the Universe and black holes. But they will not live forever. In this connection an interesting question is born. What happens when a black hole lose enough energy as a result of Hawking radiation, so that its energy density will no longer be able to maintain a singularity with an event horizon? That is, when the black hole will cease to be a black hole due to Hawking radiation?