White dwarves are a whole other thing. They are the leftover cores of supernovae. Whereas a brown dwarf is a "failed star", a white dwarf is a "failed black hole. For much the sane reasons : not enough mass.
Actually, white dwarfs are the remaining, no-longer fusing stellar cores, held up by electron degeneracy pressure, left behind when stars (such as the sun) too small to end their days in a cataclysmic supernova explosion, throw off their stellar envelopes as a planetary nebula at the end of their red giant phase. While incredibly dense, packing something in the neighbourhood of a solar mass into a sphere the size of the Earth, they have nothing on neutron stars, which fit your description better.
Neutron stars are the left-overs of some supernova explosions, where the collapsing core has enough mass that electron degeneracy pressure can't counterbalance gravity. The resulting implosion and then explosion leaves behind an ultra-dense object, packing up to several solar masses into an object with a radius of around 10 kilometers. This object is held up by neutron degeneracy pressure, the electrons and protons having been forced to combine into neutrons by gravity.
When even more massive stars explode in a supernova or even a hypernova, the remnant, too massive to be held up even by neutron degeneracy pressure, will be a black hole.
However, some very massive low-metalicity stars, of at least 130 solar masses, may end their days in a pair-instability supernova, where runaway thermonuclear fusion in the core blasts the entire star apart, leaving behind no remnant.