Tarellian starships (also referred to as Tarellian plague ships) were vessels used as late as the 2360s to carry Tarellian refugees, following the Tarellian Civil War. These ships were equipped with warp drive and transporter technology.
Nearly every star system that the vessels entered either turned them away or destroyed them, through fear of spreading the Tarellian plague. By the early 2360s, there was only one of these ships known to still exist.
In 2364, the USS Enterprise-D encountered the last surviving vessel, and its sparse crew. On board the Enterprise-D at the time, Wyatt Miller joined the last of the Tarellian crew, hoping that he would, some day, find a cure for their plague. (TNG: "Haven")