The Rat-Thing was a Thing which first assumed the form of a chunk of an unknown thing, which thawed out and ran off before attacking the rat it would later take the form of.
The Rat-Thing was first spawned when a research team accidentally broke off part of an unidentified Thing, but did not notice. While the corpse of the unknown thing was frozen in liquid nitrogen, the broken off part of the thing thawed out. The chunk roamed the station before coming across a rat, which it attacked and assimilated. After an unknown amount of time later, it encountered an unidentified female crew member (presumably Arlene), which it attacked after attempting to shake the thing off her leg. The rest of its history after that is unknown.