[wcoenen]

Degeneracy pressure comes from the Pauli exclusion principle.

There is no limit to how high this pressure can go, as there are always higher energy states to occupy. (Except that for electrons at a high enough energy state, they will disappear by fusing with protons.)

For neutrons, there is no such disappearing effect, so the degeneracy pressure can keep on increasing. So how can this pressure ever be "overcome by gravity"?

Apparently at some point the degeneracy pressure itself starts to contribute significantly to spacetime curvature. This increases gravitational pressure, which compresses the neutrons, which increases the degeneracy pressure, which increases curvature, etc. No balance is possible anymore and collapse happens.

Presumably this process of ever increasing neutron degeneracy pressure continues within the black hole until unknown physics come into play.