I think the thought is that neutron degeneracy can support against the collapse for a small range of radii and upto a point. Beyond which it keeps collapsing.

The size of a black hole is usually considered to be it's Schwarzschild Radius or event horizon where the escape velocity is equal to the speed of light.

Classically, the "guts" of a black hole were considered to be the singularity point to which all mass had collapsed and which still conserved all the properties of mass (and energy by E = mc^2) but not necessarily matter.

Recent papers on the subject hint at the possiblity that the whole sngularity thing is a mathematical phantom and that the matter inside the event horizon enters a different phase and behaves very differently than matter as we know it.