Once something gets past the event horizon (the point of no return), it is inevitably sucked into the center of the black hole. This applies to light, of course. There may be an end to a black hole in the sense that it can evaporate and disappear if you wait a REALLY long time, and don't feed it anything.

Question: if you were right at the critical radius, and you fired a beam of light perfectly tangent to the black hole, what would happen to the light? If you were at that position and looked in that direction with a telescope, what would you see?

There are actually several different kinds of black holes.Some spin and some are "charged" and some are just ordinary. When light falls into a black hole different things can happen to it, but most likely it will fall all the way to the center of the black hole and become part of it. What other things do you think can happen to light in a black hole?

Black holes do have an end of sorts. Matter and light fall into the black hole and add to its mass. It was just discovered within the past 30 years or so that black holes actually 'radiate' away their mass, often with two oppositely-pointed jets of light. Over a very long time, billions of years, a black hole could radiate away all its mass and cease to exist.

Anything that enters a black hole is lost. There is a boundary around a black hole called the "event horizon". Anything that enters collapses to a single point in the center. That's the end of line.