Those potential expenses are one reason some Medicare beneficiaries look for additional protection through Medicare supplemental insurance, or Medigap. So, who exactly qualifies for Medicare supplemental insurance? Who qualifies for Medicare supplemental insurance? Medicare supplemental insurance, or Medigap, is designed to help cover certain out-of-pocket costs that Medicare doesn't pay. That's because Medicare Advantage replaces Original Medicare as the way you receive your Part A and Part B benefits, while Medigap is specifically designed to supplement Original Medicare.