Neutron degeneracy pressure and the Schwarzschild radius

Does the Schwarzschild radius exist at the exact tipping point where neutron degeneracy pressure fails?

For example, consider a hypothetical neutron star that is being held up just below the limit of neutron degeneracy pressure. If the neutron star gains enough mass (assume a constant radius), it will collapse into a black hole. Does neutron degeneracy pressure fail at the exact point where the neutron star gains enough mass appropriate for the resultant black hole's Schwarzschild radius (where the escape velocity = c)? If so, why do these seemingly unrelated limits match?

Or... does the existing neutron star's radius exceed the resultant black hole's radius? In other words, does neutron degeneracy pressure fail, and as the the neutron star's radius decreases when collapsing, does it eventually reach a smaller (than in the previous scenario) Schwarzschild radius? If this is the case, what is the "in-between" state of matter as the neutron star collapses into a black hole?

Thank you!

• Theoretically there can be quarks stars between neutron stars and black holes and then it's the quark degeneracy that further resists the inward force of gravity. en.m.wikipedia.org/wiki/Quark_star – Triatticus Aug 31 '18 at 15:12