The Tangut Kingdom (the Xi Xia Dynasty) had submitted to the Mongol Empire in early 1210 after a short invasion, and spent some years fighting alongside their new masters against the Jin Dynasty. But, internal resentment at serving the Mongols, the expensive warfare and then Mongol demands to send troops to aid in the Mongol invasion of Khwarezm led to the Tangut seeking peace with the Jin Dynasty in 1223, while Chinggis Khan was absent in Central Asia.
When Chinggis Khan returned to Mongolia in 1225, he gave the Tangut a chance to save themselves, by sending a royal hostage to reaffirm their vassalage. In most accounts, the Tangut fail to comply, although a few surviving Tangut documents describe them sending the Tangut King's young heir, who was promptly killed by the Mongols. Nevertheless, Chinggis ordered an invasion of the Tangut Kingdom, departing Mongolia at the end of 1225 and arriving in Xi Xia in early 1226. Swiftly but methodically, the Tangut Kingdom was overrun, their cities and districts falling one by one, leaving their capital, Zhongxing (modern Yinchuan) isolated.
As Zhongxing was invested, Chinggis Khan fell ill, and would succumb to illness in late August 1227 most likely in the Liupan mountains. His final orders were to keep his death a secret until after the fall of the Tangut capital, to ensure his death would not give the defenders renewed heart. The final Tangut King submitted in July or August 1227, and upon exiting the capital (perhaps making his way to Chinggis' camp, where he was left standing outside the Khan's ger for three days), was killed, and Zhongxing sacked. Thus, the Tangut Kingdom died alongside Chinggis Khan, a great bloody send off for history's greatest conqueror.
You can learn more about the fall of the Tangut Kingdom in my recent video on the topic: youtu.be/ruyFqgY4Jog