We can't really talk about what's inside a black hole. From outside, it has a volume and a mass, and that's all there is to know.
We can say that any particle inside the horizon is inevitably headed to the center. (That's why we can't say any more: no other information can escape.) That does lead to a problem in that all of the mass would be concentrated at a single point at the center, whose density is division-by-zero.
But I wouldn't put too much weight on that. We already know from quantum mechanics that there isn't really any such thing as a "point". The math is still a problem, but the solution almost certainly lies in that direction.
We can say that any particle inside the horizon is inevitably headed to the center. (That's why we can't say any more: no other information can escape.) That does lead to a problem in that all of the mass would be concentrated at a single point at the center, whose density is division-by-zero.
But I wouldn't put too much weight on that. We already know from quantum mechanics that there isn't really any such thing as a "point". The math is still a problem, but the solution almost certainly lies in that direction.