Steve the Labrum is the cartilage between the head of the humerus and the glenoid fossa that is the receiver for the ball and socket type joint.A labrum tear will not heal because it is cartilage.Carilage has no blood supply so it can't repair.Once torn it is never going to heal. It is possible to lay flat and not cause problems if you are not real active with the shoulder.If you are real physicaly active with the shoulder then surgery is the most likely option.There is no therapy or treatment other than rest or disuse that will offer any option other than surgery.