The end stage of a star depends entirely on the mass of the initial star. If the star is less than 3 solar masses or so the star will form a red giant first then when the helium is all burned up the electron degeneracy keeps the star from collapsing further. The star that is left over after the red giant blows off its shell of hydrogen is called a blue dwarf. BTW degeneracy is caused by the pauli exclusion principle.
If the initial star is larger than that needed to make a blue dwarf, the fusion burning process will continue until iron is made, within days the core is converted to completely iron. Once iron is there the star is doomed since iron cannot be burned exothermally, the protons decay into neutrons, electrons and electron neutrinos. The shells on the outside start to fall in very rapidly since there is no more fusion in the core. When the shell hits the neutron core(held up by neutron degeneracy) it rebounds off the hard core and explodes aka supernova type II. Since neutrinos interact very weakly we can detect the burst when the protons decay in a supernova before seeing the explosion, indeed in 1987 such a neutrino event was detected shortly before supernova 1987a was detected.
If the initial mass is past another critical point neutron degeneracy is not able to hold up the core, it is at this point where a theoretical quark star would be found. This mass range would probably be very small since the next step is a black hole where no force is able to stop the collapse of the star to a point. The process involved is also VERY explosive so it would be kind of touch and go weather a star with the right mass woud stay together to make such an odd star. Also a quark star would be rediculously small and would be almost indistinguishable from a black hole from the distances which we view them.