Im a qualified sports massage therapist and injury rehabilitation specialist but not working as one so i am very rusty on details!
Ligaments have a very low blood supply - that's why they are white as opposed to muscle fibres that are pink/red - and thus they receive very low oxygen levels. This is detremental to ligaments when they are injured as the oxygen, and nutrients, in the blood are not readily available to the fibres within the ligament so the healing process is very slow, if happens fully at all. It is possible for them to heal but it takes months longer than a muscle fibre tear which can take weeks sometimes days (in the case of vital muscles like the organs).
However, i am not a surgeon so i do not know what the process is to enhance the speed of recovery of an injured ligament. I presume that technology has been developed to introduce oxygen and vital cell building nutrients into the specific area needed, how exactly i dont know! I just know how to massage an injury or during the recover from an injury, and what exercises to prescribe to increase the mobility, felxibility and strength back into muscles, tendons, ligaments and joints after injury!