Prince Tuan disappeared to the vastness of Mongolia together with the rest of the royal family...
Somehow I don't see the Imperial Court, with its enormous entourage of servants and hangers-on, and its leaders reflexively accustomed to complete luxury, and its vast amounts of physical baggage, actually "disappearing" into wilderness or desert. Such a move would require willingness to abandon nearly all personal luxuries, and endure harsh conditions under the command of some strong-minded, realistic, and capable trail boss. This crowd is incapable of that.