The Tarellian plague was a biological weapon produced by and affected the entire Tarellian race that was created and used during the Tarellian Civil War. According to Doctor Beverly Crusher, "The Tarellians had reached Earth's late 20th century level of knowledge. That's all you need if you're a damned fool. A deadly, infectious virus which at that modest level of knowledge is not difficult to grow."
Tasha Yar's security training taught that "some Tarellians made it to other worlds only to die along with the populations they infected." Geordi La Forge further added that Starfleet Academy training explained that while "many of them tried to avoid other civilized worlds as they escaped only to be hunted down and destroyed anyway." According to Captain Jean-Luc Picard, "it was believed that the last Tarellian vessel was destroyed eight years ago by the Alcyones."
By the early 2360s, the plague had all but wiped out the species, and by 2364, a Tarellian plague ship approached the planet Haven, as its crew believed the planet contained a cure for the plague. The group was successfully turned away from settling on Haven after meeting the USS Enterprise-D in orbit. During the encounter, Dr. Wyatt Miller beamed over to the plague ship with medical supplies from the Enterprise, believing it was his purpose to find a cure for the plague. (TNG: "Haven")