They would not lose him if they don't sign him. He would have to sit out of pro basketball for an entire year (not just the NBA, all pro leagues) in order for the Bucks to lose his rights, and that's not going to happen. Yi wants to play somewhere else, but if he isn't traded he will still most likely sign with the Bucks and just reiterate his trade demand next offseason.
I was replying to you, but meanwhile Yi signed. Happy for you and the NBA, this was going to be a pain in the azz.
I still believe that Yi's skillset is not so well suited for the NBA, but at least you avoided a big loss.