Buy low, sell high.
The White Sox selling off Vaughn at 50% of his trade value would be just par for the course.
And go along with getting nothing for Rodon, TA7's trade value dramatically decreased, the Madrigal trade for Kimbrel leading to Pollock leading to Benintendi (getting worse with each corresponding move), Zack Collins, Carson Fulmer, Zach Burdi, etc.
Any type of rebuild, Vaughn has more value to the White Sox than another organization until he starts getting more and more expensive in arbitration. In a way, Hahn dodged yet another bullet by Vaughn struggling enough that a team-friendly extension was never in the cards, so they saved ONE long-term commitment to their core of young players at least.
Sheets is basically just a streaky platoon guy and a poor defender regardless of where you stick him other than DH, so you can keep him around but he's not going to be one of the core pieces of the next competitive White Sox team.