Indeed, in 596, Emperor Wen created the daughter of a clansman Princess Guanghua and married her to Murong Shifu.
For reasons lost to history, there was a major disturbance in Tuyuhun in 597, and Murong Shifu was assassinated.
He sent emissaries to Sui to explain the situation and to ask for permission to, pursuant to Tuyuhun customs, marry Princess Guanghua as well.
However, later that year, the Sui official Pei Ju returned from a tour of the Xiyu states, and knowing that Emperor Yang was looking for targets to conquer, suggested to him that Xiyu states had a lot of treasures and that Tuyuhun was easy to conquer.
Murong Fuyun took his people east, entering Sui's Xiping Commandery (西平, roughly modern Xining, Qinghai) to ask for refuge and aid against the Tiele.
Emperor Yang's forces, while suffering some minor setbacks, were again able to send Murong Fuyun fleeing, reaffirming Sui's control over the Tuyuhun lands.
Little is known about Tuyuhun's status under Murong Fuyun the next several years, but at the time, Sui itself was collapsing, engulfed in agrarian rebellions throughout its territory.
Emperor Taizong agreed, but ordered that the Prince of Zun personally arrive in Chang'an to marry the princess.
Apparently immediately after he withdrew, Tuyuhun forces again attacked Liang Prefecture (涼州, roughly modern Wuwei, Gansu).
In summer 635, Tang forces began engaging Tuyuhun forces, and after some minor victories by Li Jing's subordinate Li Daozong, Murong Fuyun, apparently following the same strategies he used against Duan, burned the grasses and fled.
Most of Li Jing's subordinates believed that it was dangerous to venture further without adequate grazing supplies and advised withdrawal, but Hou Junji opposed the idea, pointing out that this was the opportunity to destroy Tuyuhun.