Epsilon 119, a dead star
Dead star at the fringe of the galaxy
Surface of above dead star
A dead star, occasionally called a dead sun, was a type of astronomical object. It was an old star whose fuel has been exhausted, resulting in the ceasing of all nuclear fusion within it.
Questar M-17 was an example of such a star was found to be orbited by an ancient insectoid ship in 2269. (TAS: "Beyond the Farthest Star")
In the mirror universe, the Tholians detonated a tricobalt warhead inside the gravity well of a dead star, thus creating an interphasic rift forming a doorway into another universe. (ENT: "In A Mirror, Darkly")
In 2370, Professor Gideon Seyetik attempted to re-ignite a dead star called Epsilon 119 using protomatter. The theory was that it would cause a cascade effect transforming the star's carbon and oxygen into elemental hydrogen. He succeeded, while taking the opportunity to kill himself in order to free his wife Nidell from their loveless marriage, since the customs of her people did not allow for a divorce. (DS9: "Second Sight")
The antimatter universe contained dead stars too, for example Amphion, counterpart of Beta Niobe. In 2270, it unexpectedly went nova, and a gateway to the regular universe opened up, apparently by Beta Niobe going nova at the same time. (TAS: "The Counter-Clock Incident")
No defined object called a "dead star" currently exists in astronomy, but stellar remnants, which include white dwarfs, neutron stars, and black holes as well as a variety of theorized and highly exotic objects, such as black dwarfs, might be considered dead stars in the literal sense.
The star which Psi 2000 orbited, said to have "went dark", might also qualify as a dead star.