What they found was that training the "trained" or uninvolved arm resulted in strength increases in the "non-trained" or involved arm with actually doing any work with that arm. They found the greatest increases in strength occurred in both internal and external rotation. There was also improvements in scaption (although they were not significant).
Take Home: If you are injured and have to immobilize your leg or arm or specific joint there is always something you can do or be working on to help speed your recover. Always try and move the body part (as instructed by your medical staff) or body parts around them if it produces NO PAIN. Secondly, train the opposite limb and specifically the muscles that will be most affected by the immobilization and you will get the benefit of this cross over training.
At Home Resistance
tubing strength training increases shoulder strength in the trained and
untrained limb
C.R.A. Magnus
Scan J Med Sci Sports
2014: 24: 586-593