There are two major ligaments that criss-cross inside the knee joint to give it stability. One is the anterior cruciate ligament (ACL) and the other is the posterior cruciate ligament (PCL).
ACL tears don't regenerate tissue and heal on their own. In minor ACL injuries surgery may not be needed. Instead knee rehab is used to regain motion and strengthen the muscles around the knee. More serious injuries may need surgery to repair or reconstruct the torn
Unlike the ACL, the PCL does have the ability to heal. This has been shown with MRI studies. Healing does depend on how severe the injury is--more severe injuries may need surgery to improve laxity.
Without surgery it's not clear yet how long the healing process takes. The PCL doesn't return to normal but motion, strength, and control are regained.