The dead Red Dwarf slowly cools to become a Black Dwarf. I say "theoretically" because …

Brown dwarfs cannot fuse ordinary hydrogen but may fuse some other isotopes like deuterium.

What most people think of when they hear “dwarf star” are brown dwarf, red dwarf, and white dwarf stars. And a black dwarf is a stellar remnant of a red dwarf that becomes a white dwarf after it loses it's fusion in the core, and then loses it's … Sometimes slightly more massive stars are included, but our Sun is definitely too massive. The dwarf terminology gradually expanded to mean “not giant” stars of any colour, and the line between “giant” and “dwarf is somewhat poorly defined; the Sun is technically a "yellow dwarf” star.

Red dwarfs generally have between 7.5% and 50% of the Sun's mass. A brown dwarf is a very small star; a white dwarf is a dead star. A dwarf star is a star of relatively small size and low luminosity.Most main sequence stars are dwarf stars. Unlike regular stars, brown dwarf stars are not massive enough to fuse hydrogen in their cores, but are massive enough to fuse deuterium. So a brown dwarf is basically a massive gas giant.

"Brown dwarfs are the missing link between gas giant planets like Jupiter and small stars like red dwarfs," Ian McLean, an astronomer at the University of California, Los Angeles, said in a statement. The term was originally coined in 1906 when the Danish astronomer Ejnar Hertzsprung noticed that the reddest stars—classified as K and M in the Harvard scheme could be divided into two distinct groups.

A red dwarf is a low mass Star that fuse ordinary hydrogen like our Sun, but only at a very low rate. They are either much brighter than the Sun, or much fainter.