A stellar core fragment is a massive remnant of a collapsed star – part of the original stellar core – thrown out into space during the process of the star's collapse. The density of a fragment can exceed 10 billion metric tons per cubic centimeter, causing it to have immense gravity.
In 2364, the SS Tsiolkovsky was observing the collapse of a red giant into a white dwarf when the gravitational influence of the star caused an outbreak of polywater intoxication that claimed the crew. The USS Enterprise-D, responding to the Tsiolkovsky's situation, was threatened by a stellar core fragment thrown off by the collapsing star. The Enterprise managed to buy enough time to repair its engines and escape by pushing off from the Tsiolkovsky using a repulsor beam. The Tsiolkovsky struck the fragment and was destroyed. (TNG: "The Naked Now")
The Genome colony of Moab IV was menaced by a stellar core fragment in 2368, when one passed through the colony's star system and its gravity produced earthquakes greater than what the colony's biosphere was designed to withstand. The colony survived with assistance from the crew of the USS Enterprise-D, who reinforced the colony dome and used a multiphase tractor beam to slightly divert the fragment's path. (TNG: "The Masterpiece Society")