A stellar core fragment is a highly massive remnant of a collapsed star, thrown out into space during the process of the star's collapse. The density of a fragment can exceed 10 million metric tons per square centimeter, making it sufficiently massive to cause enormous gravitational disturbances that can have disastrous consequences.
In 2364, the USS Tsiolkovsky was observing the collapse of a red giant into a white dwarf when the gravitational influence of the star caused a case of polywater intoxication aboard the vessel. The USS Enterprise, responding to the Tsiolkovsky's condition, was nearly destroyed by a stellar core fragment thrown off by the collapsing star. (TNG: "The Naked Now")
The colony of Moab IV was menaced by a stellar core fragment in 2368 when one passed through the planet's system and its gravitational wake threatened to produce earthquakes larger than the colony's biosphere was designed to withstand. (TNG: "The Masterpiece Society")