First, let me state for the record that I'm not an astrophysicist, nor do I even play one on TV. $:-)
That said, to answer your first question, no, the asteroid belt has nothing near stellar mass. In fact it, along with every other bit of matter in Sol's neighborhood, including all planets plus everything in the Kuiper Belt and the Oort Cloud, could easily reside within the sun's existing diameter. So nothing to worry about there.
As for black holes and the effects of their event horizons (Schwarzchild Radius), well, no one knows for sure. Physics as we understand it ends there, because once gravity has overwhelmed all the other forces in nature, theory contends that there is nothing left to prevent mass from collapsing to infinity. Nature tends to abhor infinities, though, and the fact that singularities do have mass tells us that something is still there.
As I understand it, when matter hits the event horizon it is compressed instantly (to our time scale -- at the event horizon it would appear as taking forever). This terrific change in density heats the consumed matter to billions of degrees and unleashes an enormous burst of energy mostly in the X and Gamma Ray bands, so not all the matter that falls into a singularity actually makes it past the event horizon. But the vast majority does, since gravity has no negative state. Even though these bursts of energy will equal an average star's total output for a thousand years in a single second, remember that this energy is being derived (if I'm not mistaken) from total mass/energy conversion, so a little matter makes for a lot of X-Rays.
I think what you are speaking of is the phenomenon of 'Hawking Radiation', where particle-pair created at the edge of the Schwarzchild Radius are separated -- one falls in and the other flys away in the opposite direction. This effect is constant at the event horizon because black holes are so dense that the EM fields surrounding them can generate matter out of empty space. It is through this process that black holes can literally evaporate over time if not fed, something that smaller singularities are more prone to because of their higher surface-area to volume ratio.
And the fact that this too can occur does, to me anyway, remove any theories that matter entering a black hole "exits" our spacetime continuum -- it remains here, although in a state that we cannot observe and theory can only guess at.
Thanks for this explanation, Joe. It makes a lot of sense. ~S