I had an arthroscopic test done on my wrist. It showed a torn dorsal radial ligament. What happens to these if they aren't repaired surgically?
You may be referring to the dorsal radiocarpal ligament (DRCL) across the back of the wrist. The natural history of injuries to this area remains unknown. There aren't enough studies on this topic to follow patients over time to see what happens.

From the few studies published, it appears that conservative care should be tried first. A hand therapist can apply heat, mobilization, splinting, or other modalities to help the tissue heal or to stabilize the wrist. Once the pain has been taken care of, then range of motion and strengthening exercises are usually added. A trial of six months of nonoperative care is usually advised.

If this treatment is not successful, then surgery may be needed. Your surgeon was probably able to find the areas and extent of damage with the arthroscopic exam. Surgery can be done using an arthroscope, but sometimes an open incision is needed when extensive reconstruction is required.