do black holes tend to an equilibrium state?

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I was thinking about this.
A black hole it's created given a certain mass at a certain volume (enough density), when this occour event horizon begin to form and as we know nothing can escape from it.
Now, we also know that black holes emit Hawking radiation given the zero point energy thus the black hole start loosing it's mass.
My questions are:

>Does the black hole shrink loosing it's mass in order to continuing exist?

>Might occour that the black hole after loosing to much mass become unable to sustain the gravity required by the event horizon? And what would happen in this case?