I am on long term disability for cancer treatment, which I completed May 2023. I also have a massive tear in my rotator cuff. Wondering if I go to work for a different company than the one I am currently employed at, would it affect my long term disability claim if I were incapable of working, due to effects from treatment and the rotator cuff damage? Also, would the rotator cuff tear qualify me for permanent disability, if I were unable to perform my duties at work? Thank you.

By returning to work in any capacity, your LTD benefit would generally be affected. They may be ended, or the insurer would be entitled to a credit for any income you receive.
If you are disabled from working in your own or any occupation, and have medical support stating that, then yes, you may qualify for total disability as due to that injury.
Ultimately, if your insurer does try to say that you're not disabled or that you can return to work before your doctors agree to it, please contact us ASAP and we will help.