The destiny of all matter that falls into a black hole is to get crushed to a point of zero volume and infinite density a singularity. General relativity also implies that our expanding universe began from a singularity. A singularity marks a point where the curvature of space-time is infinite, or, in other words, it possesses zero volume and infinite density.
General relativity demands that singularities arise under two circumstances.
First, a singularity must form during the creation of a black hole. When a very massive star reaches the end of its life, its core, which was previously held up by the pressure of the nuclear fusion that was taking place, collapses and all the matter in the core gets crushed out of existence at the singularity. Second, general relativity shows that under certain reasonable assumptions, an expanding universe like ours must have begun as a singularity.