This is a very good question, and the answer is that no one knows. This is a great puzzle in physics. One answer is that it radiates all away (so that all the energy of the black hole goes into the light particles, etc, that radiate out of it). The problem with this answer is that it seems like it might violate quantum mechanics, which explains how fundamental particles interact and behave. Another answer is that there is a piece of black hole left over, called a remnant, that does not radiate, but not many physicists who study black holes believe that.
So, the answer is not for sure. However, string theory, which is a theory of gravity, quantum mechanics, and all of the physics of fundamental particles, suggests that black holes can radiate away completely and not mess up quantum mechanics. This would be a great thing, but the question is not totally answered yet.
I should note that the black holes we see in astrophysics, like the giant ones at the centers of galaxies, are much too big to radiate any noticeable amount. Black holes have the unusual property that they get hotter -- and radiate more -- the smaller they are.
Finally, if you want to learn more about string theory, you might try reading "The Elegant Universe" by Brian Greene.
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