What happens when a black hole evaporates?

Because they emit Hwaking radiation from their event horizon, black holes separated from a continuous source of new mass to eat do eventually starve and die. Read more about the phenomenon, if you are interested. Because mass dilution via Hawking radiation is such a slow process, even the smallest primordial black holes would have survived for most of the life of this universe. In fact, with tools like NASA’s NuSTAR and very large land-based radiotelescopes available, we are only now likely to be observing the death throes of black holes. Supermassive black holes would have to remain isolated from new mass for something like 10 to the 100th power years to disappear; something that will not occur before the Universe reaches heat death from entropy. So our Milky Way Galaxy’s supermassive black hole is safe from starvation for the time being. But die they do. So, when they do die, do black holes go out with a bang or a whimper?