Surgery to repair a torn rotator cuff often involves re-attaching the tendon to the head of the humerus (upper arm bone). A partial tear, however may need only a trimming or smoothing known as a debridement.
A complete tear is repaired by stitching the tendon back to its original site on the humerus.
Check out the following article for more details. https://orthoinfo.org/en/treatment/rotator-cuff-tears-surgical-treatment-options/