For interventions, what is the correct progression: should you have a patient perform closed chain exercises or open chain exercises first? My initial thought was that you should do open chain first then progress to closed chain. Exceptions would be ACL surgery where open chain is contraindicated. For example, what would be the best intervention for a patient who has fair strength after long thoracic nerve injury. Would I be correct to chose the open chain activity of supine arm overhead with weights instead of closed chain activities such as standing wall push-ups?

As far as interventions go (for this hypothetical patient), open chain activities are generally seen as a progression from closed chain activities.

Furthermore, damage to the long thoracic nerve (LTN) impairs the muscle action of serratus anterior (SA) which is partly responsible for shoulder elevation. Scapula winging is the clinical manifestation of LTN damage. LTN damage/SA compromise will make it extremely difficult (if not outrightly impossible) for the patient in your question to raise weights above his head (resisted shoulder elevation) – also a form of open chain exercise, which invalidates this option and makes the standing wall push-ups (closed chain exercise) more preferable as a rehabilitative intervention.