You can orbit a black hole like any other object, and most things do, for a long, long time. Hell, the whole milky way is basically orbiting a black hole (and a lot of other mass near the center).
A black hole would be even more difficult and require more Delta-V to fly into, if you’re in any sort of orbit. So you should definitely expect tons of stuff in orbit around them!
A black hole is just a very dense objet things can fall into if they have the right trajectory. But more often than not, the trajectory will be an hyperbola or a parabola around it, and the matter don't reach the event horizon.