It makes a lot of sense as well. One has a new owner that wants to spend, the other is a team on the rise. I'd imagine that tying those teams to specific players should help their value on the market.
I'd absolutely do this. The Sox have been able to develop relief pitching so I'm not too worried there. Leury is a serviceable UTIL when he not injured. Trading Stiever would sting, but you gotta give to get.