...but there is an effect similar to the one you describe called electron degeneracy, which doesn't have anything to do with gravity but does play a role in supernova explosions.

A degenerate electron gas occurs when plasmas are compressed into superdense states by gravity, as in the interiors of supergiant stars. The protons and stray neutrons mixed in the plasma behave like an ideal gas, i.e., they exert a back-pressure inversely proportional to the volume they are compressed in. But the electrons, being lighter, can go much faster, so they eventually occupy all the volumes in 6-dimensional phase space (x,y,z, Px, Py, Pz) allowed to them by the Heisenberg Uncertainty Principle. The Pw terms are momentum dimensions, which share the phase space with the x,y,z, space dimensions. Uncertainty Principle states no two identical particles with the same spin can occupy the same location in phase space, not normal space.

As the plasma is compressed, the electrons are prevented from gaining further momentum because those momenta (velocities) are denied to them, and the back pressure ceases. The electron component of the plasma no longer behaves as an ideal gas, no back pressure is generated to halt the gravitational collapse, and the star implodes because not enough pressure is generated to stop it. The core collapses and the outer layers of the star (still non-degenerate) fly off into the surrounding space in a colossal explosion.