When a star with mass similar to our own Sun expends all of its fuel, it settles into becoming a white dwarf. If the star was made up of frictionless, non-quantum mechanical matter, there would be nothing from stopping the star from collapsing into a black hole.
However, all matter are of a quantum mechanical nature, so if matter is packed in tightly enough, degeneracy pressure exerts itself, which is the result of the Pauli exclusion principle, where no two fermionic particles of the same type can occupy the same quantum state. In a white dwarf, electrons are packed so tightly together such that if they get packed any tighter some electrons would end up in the same quantum state, so a pressure that fights against further packing is exerted. This electron degeneracy pressure prevents the star from collapsing into a singularity.
If a star has more than 1.4 times the mass of our Sun, though, then the electron degeneracy pressure is not enough to keep the star from collapsing. Then the particles in the star combine into a homogeneous soup of neutrons, which in turn exert a neutron degeneracy pressure. For stars with up to 2 to 3 times the mass of our Sun, this is enough to prevent gravitational collapse and they exist as neutron stars.
However, neutron degeneracy pressure is not enough for stars with even larger mass. Either the star could collapse into a black hole, or the neutrons could disintegrate into free quarks, and further collapse would be prevented by the quark degeneracy pressure. The thing is that a neutron is probably about 50 to 200 times the mass of its constituent quarks, so a lot of energy should be released when a neutron star collapses into a quark star.
And now Canadian researchers may have identified supernovae explosions which may have resulted in quark stars. These explosions were about 100 times brighter than the typical supernova explosion, and they believe that the release of energy as a neutron disintegrates into its constituent quarks during the formation of quark stars could explain why they are so much brighter. If their hypothesis is confirmed, then we'll need to add one more type of star to the textbooks.