I don't think Boston would need to attach anything to Brogdon to get a trade done if they wanted to trade him. There is kind of a cloud over him right now due to the injury and the rescinded trade but that does not change the fact that he is a good player. LAC was reportedly willing to give up Morris, Amir Coffey and the 30th pick for Brogdon.
The current report on Brogdon's injury is 4-8 weeks of rest. I think if LAC had had time to confirm this, Brogdon would be in LA already. I don't think Brogdon will be traded now. The whole point was to trade one of Smart, White, or Brogdon to balance the roster. The point wasn't to trade Brogdon for the sake of trading Brogdon. The roster is balanced now, we have the reigning 6MOY returning to be our 6th man again. I will be very surprised if the Celtics dump his salary.
And if they did want to trade him but not take any salary back, it would probably need to be a 3-way, like the LAC deal, but instead of us getting a player like Porzingis, we would take back low cost prospects or something from the 3rd team.