(covers information from several alternate timelines)
An emergency core shutdown was the complete shutdown of the warp core on a Federation starship by means other than regular helm control. This procedure was rarely used, since it left the ship in question without warp power for over a week, and as such was designated as an emergency measure only.
Following a collision between the USS Enterprise-D and the USS Bozeman in a temporal causality loop in 2368, an emergency core shutdown was unsuccessfully attempted, and the resultant core breach destroyed the Enterprise, resetting the loop. (TNG: "Cause and Effect")
In 2370, an emergency core shutdown was suggested after the Enterprise began developing severe malfunctions and had gone to warp without command input. However, the vessel dropped out of warp before the procedure could be commenced. (TNG: "Emergence")