Lets look at an analogy: sound waves in water. Let us assume that nothing can go faster than sound. Sound waves in water obey very similar equations to light waves in spacetime. Now imagine that the water goes over a waterfall so virulent, that the water flows (from our point of view) faster than sound. Sound (and since nothing, by assumption, goes faster than sound in the water, also anything else) cannot escape from the waterfall. Now imagine that we are describing everything from the point of view of being inside the water, without any embedding space around that the water is flowing in. The statement that nothing can go faster than sound is a local statement, that at the point where you are, sound is what goes fastest. But still that sound cannot get out, and neither can anything else.
The equations which give us the possibility of black holes, namely Einstein's equations, also say that if you have a region like a black hole, out of which light cannot get, then within that region you must have a singularity, a region of infinite tidal forces which would destroy everything. This theorem is based on the assumption that everything must have positive energy density. We have never found anything with negative energy density (and its existence would be unstable since then, by creating that negative energy density matter, one could create an infinite amount of ordinary positive energy density matter and negative, out of nothing.) I.e., the matter which falls into a black hole does not come out anywhere, it hits the singularity in a finite, very short, time, and is lost to the universe.
People have played with the idea that perhaps wormholes could exist, but they require the existence of that negative energy density matter, for which no evidence exists.
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