In fact it doesn't. We are still at in the densities and masses of "sort of known physics". One way of thinking about it is to imagine the neutron star as a giant atom. As the gravitational pull increases, the energy levels will get closer and closer and you can squeeze more and more particles in the same energy level. Once you get close to the speed of light, then the number of available energy levels increases by a huge number, and Pauli stops keeping the star from collapsing.