What does a black hole lead to?
We don't know what a black hole leads to.
First of all a black hole isn't a hole in the usual sense that you can fall into it and possibly climb out.
A black hole is a region of spacetime which is so curved due to gravity that nothing, including light, can escape.
We have never seen a black hole directly. Black holes were first predicted by the Schwarzschild solution to the equations of General Relativity. Black holes have since been discovered, usually by large energy output, from an object so small and massive it can only be a black hole. As it would take thousands of years with our current technology to reach one, observation is currently impossible.
General Relativity predicts that inside a black hole there is a singularity. This is a point of infinite density into which ultimately anything entering the black hole must fall.
When equations of physics yield an infinity it means that the equations don't work under the conditions leading to the infinity. We need new physics to understand black holes better.
People have speculated that something entering a black hole may emerge in a different universe. It is theoretically possible to enter a black hole but it would be impossible to return and report what happened.