The first or one of the early Hidden in Plain Sight books postulates that gravity is not exactly the equation we use now, the equation that results in a “singularity.”
It postulates that at extreme levels, gravity “balances,” pushes back on itself, and that the mass of a black hole is not concentrated at a point, but is (for want of a better visual image) a hollow sphere at the event horizon.
There is also the possibility that the collapse does cause the mass to be compressed to zero size. There may be another type of degeneracy (something like the Pauli exclusion principle) that prevents the matter from being compressed to zero size.