The last stage of stellar evolution is a black dwarf. Because they emit no heat or light, these objects would be a challenge to detect if they existed today. However, at less than 14 billion years old, the universe is still too young to have created any black dwarfs!
A main sequence star that lacks the mass necessary to explode in a supernova will become a white dwarf, a 'dead' star that has burned through all of its hydrogen and helium fuel. But the white dwarf remains hot for some time, much like a stove burner still emits heat even when it has been turned off.
After enough time has passed, all of the leftover heat will have radiated away. No longer emitting heat or light, the white dwarf will become a black dwarf, its loss making it difficult to find. However, the black dwarf would still retain its mass, allowing scientists to detect the effects produced by its gravitational field.
But there's no need to start searching for the elusive black dwarfs yet. At the moment, they are strictly theoretical. Scientists have calculated that a white dwarf will take tens of hundreds of billions of years to cool down and become a black dwarf. Even if a white dwarf had formed at the moment of the Big Bang — an impossibility, since a star must pass through several evolutionary stages that take at least a billion years total — it would still be a white dwarf today, having not yet sufficiently cooled.
Brown dwarfs, objects too small to have reached the point of fusion, were once called black dwarfs.