When a black hole eats a star -- or anything else, for that matter -- there is always residual material that's blown away, long before the event horizon, but well into the ripping to the atomic level, as well as a lot of radiation, generally in the higher beta and gamma ranges. These bits and pieces are what cause the particle jets.

Black holes are generally very messy eaters.

I recall an Asimov short story that involved a minor trapped on an asteroid who spotted a particularly small black hole passing through the Solar System. He was able to call for help by throwing stones into the black hole -- in an SOS pattern.

A clever bit of a read.