A white dwarf is a star formed when a red giant runs out of helium fuel after losing most of its mass into space.
In 2364, the SS Tsiolkovsky was observing the formation of a white dwarf star when its crew succumbed to polywater intoxication. The USS Enterprise-D, sent to investigate, was subsequently threatened by a stellar core fragment thrown off by the collapse of the red giant. (TNG: "The Naked Now")
White dwarfs are the only natural source of vertion particles. In 2370, a network emergent circuit nodes aboard the Enterprise-D collected vertions from the white dwarf Tambor Beta-6 to sustain their growth, but the supply from a single star proved insufficient. (TNG: "Emergence")
In 2383, Dal R'El unintentionally guided the USS Protostar to a binary star system consisting of a white dwarf in the final stages of tearing apart its red giant companion. The ship became caught in the white dwarf's gravity well, but managed to escape by riding the shockwave of the star's explosion. (PRO: "Starstruck")