In Layman's terms, the Pauli exclusion principal wouldn't need to be overcome to form the black hole. A Neutron star of a certain size will shrink below it's Schwarzschild radius naturally. That's not hard to see. In fact, like white dwarfs, Neutron stars grow smaller in radius as they gain mass. The maximum mass wouldn't be much more than 2.5 or so solar masses past which the Neutron Star couldn't avoid becoming a black hole.
The relativistic effects get complicated, such as what precisely happens at the 100% time dilation and beyond.
Now, as to what happens inside the black hole, there's two general points I can make. One is, as the neutrons (quark matter, whatever it is), grows more compact the weight and force to compact it further keeps increasing. That's fairly obvious. It almost becomes the unstoppable force (weight and gravitation) vs the immovable object (Pauli exclusion) question. The problem with knowing exactly what happens is essentially the singularity problem. The math breaks down. I don't think anyone knows.
Another way that I like to look at it, is Gluons, like photons, move at the speed of light. Inside a black hole, Gluons, like Photons would be drawn towards the center, not able to fly outwards and that property might greatly shrink the size of a Proton or Neutron down to the size of . . . maybe an Electron?? but again, who knows? Maybe some kind of quantum tunneling keeps the size of the Neutrons somewhat consistent but the gravitational escape velocity exceeding the speed of light could greatly reduce the more standard/observed size of the Neutrons. (I think).
I know you asked for the most accepted explanation and I've only touched on this from a layman's POV, so, hopefully someone with a bigger brain than me will answer this one more precisely to your specific question.