What is the worst thing you can do after an injury, regardless of the severity or location? Nothing. Nothing is the worst thing you can do. I’m not saying that after you have a knee injury to go and get a new squat record, but eliminating any lower body work can both prevent further improvements and actually increase future injury risk.
A study out of the University of Vermont had a group perform only 1 legged exercises for a period of 8 weeks. The average strength benefit in the UNTRAINED limb was 36% (hamstring muscles) and 58% (quadriceps muscle) of that achieved in the TRAINED limb. You can benefit from exercise without even moving the injured limb!!
Not using this injured arm/leg, can also result in increased scar tissue formation. Basically by not using the body, you are rebuilding a house with a much more fragile foundation. Therefore when stress is applied to that limb or joint (i.e. playing sports), the risk of re-injury is much greater than before.
Considering athletes are some of the world’s toughest population due to a constant barrage of obstacles, I am amazed by the reactions of so many to stop training completely or even avoid using the opposite limb of the injured area.