Not sure if this has been discussed or not, but I wonder whether restructure negotiations ever get into players asking for, and teams agreeing to, use of some of the saved cap room to acquire another player at a position favorable to the renegotiating player.
Example: Tyrod says I'll do this deal if you agree to strengthen the roster at WR or TE.
Not that this would ever be written down in contract form, but it would be interesting to hear what kind of quid pro quos go on in these types of negotiations.