Let's say for a moment that the NBA and players agree on a hard cap around 70 million that phases in over the next three seasons. An amnesty clause is put in in order to help teams adhere to the new hard cap. Should and would the Bulls use the clause?
Presently, the Bulls have three guaranteed deals totaling a shade over 40 million in three seasons:
Carlos Boozer: 15.3 million + 1 year remaining 16.8 million
Luol Deng: 14.275 million (expiring)
Joakim Noah: 11.1 million + 2 years remaining at 12.2, and 13.4 million
For arguments sake, let's assume that Derrick Rose is owed 13.4 million in this season with one season left at 14 million [based on a one year decrease in contract length and a new rule putting max contracts starting at 12 million].
The Bulls will then have about 54 million locked into those four players with only 16 million left to fill out the rest of the team.
Without a veteran exception to go over the 70 million with vet minimum contracts the Bulls would need to fill out nine roster spaces with that 16 million, or in other words, they could afford to play two players about 5.5 million a piece and then try and fill out the remaining 7 spots at the vet minimum.
You can keep two guys for depth with this line up, so two of (Gibson, Asik, Korver, Brewer, and a yet unknown SG (JR Smith, Jason Richardson, Nick Young perhaps etc..), but everyone else will be at the vet minimum.
Vet minimum fourth big man, backup SF, PG etc...
The Bulls would be freed up with considerable room the following season with Luol Deng's contract coming off the books and him possibly resigning for far less or just leaving salary space to be replaced by someone else, unfortunately, Gibson and Asik will need to be extended prior to that point, so keeping the big four means one of those guys has to leave. Same with Korver, Brewer, and Watson.
The alternative is to use an amnesty clause [if a hard cap comes into play, you can bet one will exist in some way] to stay under the cap. Who do you target?
Luol Deng is probably safe given that he's expiring anyway, so he doesn't free up much in the long haul for you which leaves Boozer and Noah as the prime candidates.
Of the two, the Bulls probably need Boozer's offense more than Noah's defense, but his pay rate is higher, his age is worse, he's more likely to decline, and his defensive aptitude doesn't fit in with the rest of the team as much.
Joakim Noah does have the additional year of guaranteed money which is perhaps the only thing working against him in this discussion.
Even so, I think Boozer is the obvious candidate in this instance. Losing his 15.3 million gives the Bulls about 31 million to spend on other players. As such, they can now take that list we pick two guys from and instead pick four to five guys.
In the end, you're probably gaining 2-3 quality depth options for Carlos Boozer if he's amnestied. Despite the fact that they need his scoring, and I believe he can perform much better than he did last playoffs, that's a choice you make if it's on the board.
Fortunately, if a hard cap does come, some version of the amnesty clause or non-guaranteed contracts will have to come with it by necessity rather than a one time use like the last agreement. As such, the Bulls would likely wait until the last minute before having to execute such a clause.