Which term describes the cooling and fading stage of a white dwarf?

The term that describes the cooling and fading stage of a white dwarf is "black dwarf." A white dwarf is the remnant core of a star that has exhausted its nuclear fuel and shed its outer layers. Over enormous timescales, a white dwarf will continue to cool as it emits its remaining thermal energy into space. Eventually, if it cools sufficiently, it will no longer emit visible light and will become a cold, dark stellar remnant known as a black dwarf.

This stage is characterized by the cessation of nuclear processes and the star's transition to a state where it is effectively invisible, as it no longer radiates heat or light. While black holes, neutron stars, and supernovae are all related to stellar evolution, they represent different phases or end products of stars that are not applicable to the state of a white dwarf cooling into obscurity.