Lecture 6. Death of Low Mass Stars
All stars eventually run out of hydrogen fuel. This marks the end of their main sequence lifetime. But gravity never runs out....!
What happens next depends on mass, but for a low mass star (mass between 0.4 and 5-6 x that of our Sun) then there is a stable state where the core of the star is held up against gravity by the purely quantum mechanical effect of electron degeneracy pressure, forming a white dwarf.
More on death of low mass stars
see Kuhn p426-441
another nice site about stellar evolution , together with a nice java simulation of the changes in luminosity and temperature (i.e position on the Hertzsprung-Russell diagram) as stars of different mass evolve.
Pictures of some lovely planetary nebulae and more on how they form
Ultimate core collapse is held off by electron degeneracy pressure, a purely quantum effect. Electrons belong to a class of particles which like to be alone! Two electrons with identical energies cannot go in the same box. This is just the way they are. This is what stabilises a white dwarf against gravity (page 3 of this is specifically about electron degeneracy pressure.