Kuchlug, the deposed Khan of the Naiman confederation that Temüjin defeated and folded into his Mongol Empire, fled west and usurped the khanate of Qara Khitai (also known as the Western Liao, as it was originally established as remnants of the Liao dynasty).
Who took control of Qara Khitai after fleeing Temüjin's Mongol Empire?
Kuchlug