The natural history (what happens) to an unrepaired rotator cuff tear depends on several factors. The size of the original tear, the cause (trauma versus degenerative soft tissue changes), and your activity level since the tear can all make a difference.
The body does try to repair the damage. If the tendon pulls away from the bone too far, then the body fills in the gap between the end of the torn tendon (called the tendon stump) and the bone where it normally attaches. Scar tissue and fat cells are used to accomplish this fill-in work. The process is called fibrosis and fatty infiltration.
The longer the time interval between when a person injures the rotator cuff and surgery to repair the damage, the greater the risk of fatty inflitration forming and muscle atrophy (wasting and weakness).
So in a way, you could say this is “normal” — in other words, the natural course of events. But it is not a healthy result and may require surgery to repair the damage.