Okay, lets imagine that we travel into the future and the sun dies off and all that remains is the white dwarf. It is my understanding that over time it will eventually cool down and fade. Is there anything that follows afterwards?

 The Sun will form a planetary nebula. How intricate we don't know. Maybe once the white dwarf dies the gas will condense and form another protoplanetary disk.

If the star orbits a more massive star, and very closely, then it's destined to become a Type 1 supernova: matter from the larger star will spiral onto the surface of the dwarf, periodically flashing into brilliance as the dwarf's mass limit is passed, then finally exploding altogether and flinging its contents into space.

Otherwise, the most likely fate is a slow fading to the point where the dwarf's temperature is only a degree or two above absolute zero. By this time, the other bright stars in the galaxy will have run their course and the only visible illumination will be the dull glow of the remaining red dwarfs.

WOW! - I've been wondering about this, for QUITE some time! - not only was this information helpful, but it was also rather insightful! - Thx for keeping me 'in-the-loop', about white dwarf stars! -drew =P