If the joint is weak, loose or unstable the goal would be to tighten it up. Proper assessment of muscle balance, lengths, relative strength etc can lead to a corrective exercise program to strengthen the shoulder gurgle. If the ligaments are too long there is not much you can do with them - so you can tighten the related muscles and must do so in a balanced manner.

Starts in the core though. There is a criss cross of facial activated (tightened) when the core is activated that runs across the back connecting the shoulders and hips. Activating the core stabilizes the shoulder (and hip). This can be demonstrated in minutes.

Core function is ruined by excessive sit-ups and poor exercises.
The body takes the path of least resistance. Sit-ups flex the rectus abdominus (6 pack). When over trained compared with the inner obliques and TVA (some of the main core muscles) the body activates them, from you trained conditioning, when trying to stabilize. All movement (if body functioning) starts at the core.
The core pulls the belly button INWARDS and activates the fascia stabilizing the shoulders.Flexing the rectus pushes the belly button OUTWARDS. If an imbalance in strength and function of abdominal musculature then when the body tries to stabilize it will go to the over trained and over activation of the 6 pack.

Think what happens to your biceps when you flex - they shorten and bulge. Flexing the 6 pack bulges it OUT and pulls belly button out (unless balance with other abdominal muscles and have proper core function.

What you eat strongly affects core function.

All the viscera are connected through the spine to muscles and visa versa. What this means is that any problem with your internal organs will inhibit related muscle function.

example

heart attack - it is felt in the muscles of the left shoulder/arm/chest etc
The heart and those muscles connect at the same spinal segment(s) and the heart problem is experienced by the effected muscles.

What happens is the heart sends info to the spine saying - got a problem here. The spine sends the info to the brain saying - got a problem here - the brain sends info back saying - act like you have a problem... Now what happens here is the info to act like you have a problem goes back to the spinal segment(s) but instead of the info going only to the heart it goes to everything connected to that spinal segment(s)... including the skin, organs, muscles etc

When food is eaten that inflames the gut and digestive organs they send the info to the brain saying - got a prob here... brain says to act like you have a problem and core muscles (which are needed to support shoulder girdle) act like they have a problem and don't function properly...

Muscles are only as strong as your internal organs.

Assessing core function is a huge starting point along with the structure of the shoulder etc The body works as a whole and looking at the problem area is often looking at a symptom of imbalance and not the cause.

Digestive health is HUGE when it comes to core function...
Never mind we have trained and conditioned the core not to work by not knowing how to work it properly.

Proper assessment and program design for rehab includes looking at the core and that means digestive health etc in my opinion.