Can a torn labrum (left shoulder) heal itself?

No: Generally labral tears do not heal on their own. However if there is no pain and no feelings of instability then no treatment is needed. If therapy does not work then surgery is sometimes needed to repair the labrum.

Yes: Not all labral injuries are the same. Acute or recent injuries protected appropriately from reinjury have a better chance to heal than chronic or older injuries. Most are treated with an initial course of rest then physical therapy. Only the persistent, symptomatic labral tears may warrant surgical intervention eventually. The final decision is best made between you and your surgeon.

Its Possible However: If it does not heal, you might want to consider platelet or stem cell therapy. So far the only practice that has significant research and patient base regarding stem cell therapy is Regenexx Physicians Network. They have over 6500 patient registry with pretty good results. Check out Regenexx.Com.