A rotator cuff muscle prevents downward dislocation of the humerus?

Primarily (90% of the time, especially in a resting position) this job is performed by the supraspinatus muscle, and is assisted slightly by the infraspinatus and teres minor. When you are lifting something, or actively using the arm it tends to be the larger deltoids muscle that will kick in and keep the humerus from displacing inferiorly.