The popular description of black holes, especially outside the academia, is that they are highly dense objects; so dense that even light (as particle or as waves) cannot escape it once it falls inside the event horizon.

But then we hear things like black holes are really empty, as the matter is no longer there. It was formed due to highly compact matter but now energy of that matter that formed it and whatever fell into it thereafter is converted into the energy of warped space-time. Hence, we cannot speak of extreme matter-density but only of extreme energy density. Black holes are then empty, given that emptiness is absence of matter. Aren't these descriptions contradictory that they are highly dense matter as well as empty?

Also, if this explanation is true, it implies that if enough matter is gathered, matter ceases to exist.

(Sorry! Scientifically and Mathematically immature but curious amateur here)