One thing I never understood is, how does a black hole evaporate, even via hawking radiation? Doesn't the matter it ejects just fall back in?
For a more detailed answer with references, see the last answer here at https://physics.stackexchange.com/questions/89983/how-many-o... .
Because one part of a pair of virtual particles crosses the horizon, and the other one does not, they become separated by said horizon and cannot recombine and disappear. The particles become actual and not virtual, but one is lost to the hole. Hence, it looks to the external world as if a particle was emitted by the hole.
Note that to my (layman's) knowledge, this has not been actually observed, but does seem to be a modern consensus and involved a paid bet.
Ultimately, hawking radiation does not come from within the event horizon, so it can escape into the wider universe.