The rotator cuff doesn't heal itself. But that's not usually the question the patient is asking. Patients want to know if they can get a comfortable, functional shoulder without surgery when there's a tear. And the answer to that is often yes.
The mainstay of non-operative treatment is structured physical therapy. This addresses symptoms, improves range of motion, strengthens remaining cuff muscle, and trains other muscles (deltoid, scapular stabilizers) to assist in moving the arm. We may also add activity modification, anti-inflammatory medications and therapeutic injections. When a rotator cuff tendon is partially torn and inflamed but has not pulled completely away, platelet-rich plasma (PRP) injections become an option, depending on the exact injury and diagnosis.
Therapy will not, however, shrink a tear or keep a tear the same size. Some patients with small tears go many years without pain or significant limitation of function. But tears can get larger. They can pull away even further from their insertion site, and the muscle can degenerate in a way that makes repair more difficult down the line. So non-operative treatment is a treatment choice, not an absence of treatment. Certain factors should make us more concerned that conservative treatment won't be enough: measurable weakness, a tear resulting from a specific injury, and imaging evidence of a high grade partial or full thickness tear. Others include a retracted tendon, plateauing improvement despite an appropriate course of therapy, and sports or occupation requiring strong overhead function.
If these factors aren't present, then it's reasonable to give conservative treatment a shot. If they are present, then maybe the question isn't, "Can I avoid surgery?" but rather, "What am I risking by not getting surgery now?"