It is the surviving core of the star where fusion turned H and He into Carbon. While a star, fusion generated heat a pressure to withstand gravity. The answer is electron degeneracy , which we discussed before. Electrons can only be pushed so close together and then no more. Inside the white dwarf, the electrons have reached this degenerate limit and cannot be compressed any more, gravity is stopped.
White dwarfs do exist.
White dwarfs start out very hot . Because of their low surface area, white dwarfs have a low luminosity, they lose energy only very slowly. They take forever to cool off. Eventually they will cool until they emit no more visible light. Then they are called Black Dwarfs.