The phrase torn rotator cuff covers a multitude of injuries. Firstly there are four muscles in the rotator cuff, any one of which can be torn. Secondly there are degrees of tear and finally, how you tear your rotator cuff can influence the treatment and how it responds to therapy.
Think of the tendons of this group of muscles as an old rope that you have kept in the trunk of your car and used occasionally for towing. It could break for several reasons. It could simply fray over time because of age and over use. If you relate this to a torn muscle, this could be a fairly easy tear to fix as it has happened quite gently, the trauma to the muscle is slight and it may be that simply rest and exercise would be enough to fix it.
If on the other hand your rope snapped because you tried pulling something that was too heavy, it could have snapped clean through or stretched, pulling the filaments apart. Relate this to a shoulder injury and you could be looking at something that needs surgery to fix a bad tear or complete break.
Putting aside my old tow rope, whenever tendons join to bone there is a possible weakness. Lifting too much weight or lifting badly can cause the tendon to become detached or a piece of bone to break away. In this case you would almost definitely be looking at surgery as part of the treatment.
Another cause for possible surgery is a shoulder impingement. This is caused when an injury causes the tendon to become inflamed. As it swells it becomes trapped under the collar bone. If rest doesn’t reduce the inflammation it may be necessary to operate to shave away a piece of bone to free up the trapped tendon.
The good news is that most shoulder injuries are soft tissue damage and don’t involve bone damage so a lot are curable with rest and exercise in that order. Rest to allow the muscle or tendon to heal and exercise to start strengthening them again. Never try working through a shoulder injury as it will almost inevitably lead to more damage.
Although treatment may well involve anti-inflammatory drugs and pain killers be careful not to overdo it with these and mask the symptoms as this can lead to further injury simply because you are hiding the problem rather than dealing with it.