What happens to the matter that falls into a black hole?
There are theories as to what happens to matter which falls into a black hole but we can't be certain.
First of all when matter falls into a black hole it has to pass the vent horizon. This is the point where not even light can escape.
If the hole is not really large, anything approaching the event horizon will get torn apart by gravitational tidal effects. The tidal effects result from the fact that the gravitational pull on the end of an object nearest to the black hole are significantly larger than the gravitational pull at the end furthest away.
There is another problem involved with crossing the event horizon called the information paradox. If all information about the state of the matter is lost when it crosses the event horizon that breaks our laws of physics. Though Stephen Hawking has a theory that the information is somehow stored in the vent horizon.
Assuming matter gets past the event horizon intact then it is destined to reach the singularity inside the black hole. This is a point of infinite density which causes our laws of physics to break down. The matter would be consumed by the singularity if it exists.
We need a quantum gravity theory to answer what happens inside the black hole. This is not going to happen soon.