The NBA Bird Rule lets teams exceed the cap in certain situations in order to resign their own free agent players. It has nothing to do with injuries, player performance after an injury, or the affect of guaranteed contracts on the cap. Rather, it is a mechanism NBA teams can use to keep their roster together.
A parallel with the Rams would be Littleton, not Gurley. If the NFL had a 'Bird Rule' they could exceed the cap in order to resign Littleton.
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