First look at 4 CFR 21.6: Withholding Award, Suspending Contract Performance, Override of Stay, Injunction
B first got a CICA stay to stop work; which the agency defeated with its urgent and compelling and public interest talk to continue work; then B wanted to continue stoppage of work and went to the COFC which could stop work.
The COFC has 4 thresholds it reviews to issue an injunction. It doesn't take an injunction lightly. In my scenario, It found something wrong with the proposal evaluation and determined an injunction was needed to stop performance. I'm assuming it did find that something.
A could appeal the COFC opinion to the Court of Appeals for the Federal Circuit which could overrule the COFC opinion and knock down the injunction.
At first, I was trying to find a way of defeating Contracting Blackmail. I couldn't eliminate the possibility in it entirety because of the COFC. Then you have the CAFC that can reverse the COFC. This is absurd. In the real world time is money. The longer B has avenues to stop contract performance, the more B has the possiblity of someone paying him off to go away and withdrawal court action.
I've been a proponent of removing the courts from hearing bid protests. This seems to support their removal--if my scenario is possible. With GAO only in the bid protest arena, a CICA stay is granted until the GAO decision. If GAO denies the protest it's over. The agency can still ignore the stay and continue performance. There just won't be anyone hearing protests over the stay.