First: “Orbiting the center” implies movement in circles and ellipses, and thus implies angular momentum. Angular momentum is a conserved quantity. If the collapsing star didn’t have it, the black hole’s contents won’t spontaneously develop it. Some black holes do have it, but not all.
Second: under general relativity spacetime is biased so the three direction “future” is pointed to the center of the black hole. This is true of any mass, but in the black hole it is so intensely pointed that even traveling through the space part of spacetime at the maximum possible speed (the speed of light) isn’t fast enough to escape that, not in any direction. Perhaps the fastest moving objects at the very edge of the region of space we call the “event horizon” could fall in slowly enough that the black hole evaporates around them? I dunno, I don’t have math for it. But even then I wouldn’t count on it for the general case.
Better to imagine everything crushed as it is dragged to the center - perhaps first into neutronium, and then quarkium, and then something hard to say except that it’s all a giant high-energy mess.
Inside the event horizon you’d need to orbit faster than the speed of light. Outside the event horizon - if the matter wasn’t in orbit before then it can’t magically gain momentum to be in orbit.
I don't think black holes are what is being described here, but no, it would not fundamentally be all that different from a binary system orbiting around a shared center of gravity between the two objects.
