Almost all policies have a "preexisting illness exclusion." This sets a time following the policy purchase during which there's no coverage at all for any medical condition a person was treated for within some period just before buying the policy. Six months before and after buying the policy is the standard exclusion period. A shorter exclusion period usually means a higher premium.

Regardless of someone's medical history or current medical condition, if she has "guaranteed enrollment" in medigap, she can buy any policy sold in her state. Or she may have limited guaranteed enrollment in certain but not all policies, if she lost her existing coverage with a Medicare Advantage managed care plan.

If she doesn't have any guaranteed enrollment, either because she waited too long to buy her first medigap policy or because she's now switching policies, an insurance company may refuse to sell her a policy or may charge her higher premiums because of her medical history. The company could ask to examine her medical records and even have her undergo a physical exam by an insurance company doctor.