An MRI revealed a ligament tear low right abdomen, held together by scar tissue. Chronic injury doc said. Can this improve without surgery?

Injury. The scar is the normal way the body heals, so presence of scar is normal. Generally, if the injury is greater than a year old, then the healing and the re-modeling of the wound is complete. Both form and function are stable and will only vary little as time passes. Often, surgical revision of the scar leads to improved appearance and may lead to better function of the muscles involved.
Yes. "Sports hernia" In most people the scar tissue will fibrose and the pain will resolve over time. It's important not to"re-injure" the area. Has your doctor talked about "sports hernia"?