The Alliance Remnant, also called the Alliance-in-exile, or simply the Rebels, was a government-in-exile formed from the Alliance to Restore the Republic following it's disastrous defeat at the Battle of Endor in 4 ABY, resulting in the deaths of Leia Organa and Han Solo, as well as the fall of Luke Skywalker to the dark side. The government fought the Empire in the two-year Continuation War, which lasted until 6 ABY. By that point, much of the Remnant was destroyed, Mon Mothma was killed, and as were much of the other Alliance High Command members. The Remnant was in chaos much of the time, several officers of the Alliance military decided to leave and go rogue or defect, and thus it was on the defensive. It's resources were also lower than that of the Rebel Alliance, as much of the main fleet was destroyed at Endor.
After their defeat at the hands of the empire with their attack on Orion IV, the Remnant collapsed entirely, though some individual units and ships continued resisting the Imperial authorities. They became known as the Alliance holdouts, not being a unified government like the Remnant.