People age 65 who have Medicare Parts B are eligible for a Medicare Supplement plan. You may also be eligible for a Medigap policy under the following cases: Under age 65 who have a qualifying disability and received Social Security Disability Insurance (SSDI) benefits for at least 24 months. Any age diagnosed with certain terminal illnesses, including End-Stage Renal Disease (ERSD) and Amyotrophic Lateral Sclerosis (ALS).