Or, apparently, if it crosses an event horizon, although I've never properly understood how that works. (Explanations I've found typically just say: "All paths from a black hole are toward the black hole."

Most things flying towards a black hole don't cross the event horizon thanks to angular momentum.

Stars tend to get torn apart, go into the accretion disk, and then eventually fall in. But we don't have a big black hole in the solar system.

For present purposes the Newtonian approximation suffices, and in Newtonian gravity there are no black holes and no event horizons.