ultimately what happens to such stars?
A white dwarf is stable once formed and will continue to cool almost indefinitely, eventually to become a black dwarf
White dwarf
A white dwarf is stable once formed and will continue to cool almost indefinitely, eventually to become a black dwarf. 
which of the following will never undergo fusion in any star White dwarf when was the first time such a star was spotted? 1910
wiki:19666796
White dwarf [SEP] Fate
A white dwarf is stable once formed and will continue to cool almost indefinitely, eventually to become a black dwarf. Assuming that the Universe continues to expand, it is thought that in 10 to 10 years, the galaxies will evaporate as their stars escape into intergalactic space. White dwarfs should generally survive galactic dispersion, although an occasional collision between white dwarfs may produce a new fusing star or a super-Chandrasekhar mass white dwarf which will explode in a Type Ia supernova. The subsequent lifetime of white dwarfs is thought to be on the order of the hypothetical lifetime of the proton, known to be at least 10–10 years.