The phrase "to stabilize the joint" means to make the joint more steady and secure by strengthening the surrounding muscles, ligaments, or other supportive structures. Full definition
A strengthening program to help you develop the muscles around the shoulder which are responsible for stabilizing the joint is usually recommended. (sportsinjuryclinic.net)
This helps better stabilize the joint and, I find, helps reduce and eliminate pain and discomfort from the pressing movement. (fitstep.com)
This makes for an unstable joint and the body's attempts to stabilize the joint only end up yielding arthritis. (vin.com)