It depends. If you are applying for a Medigap policy during your initial Medicare enrollment period, then regardless of your past or current health problems, you are guaranteed the right to purchase any Medigap policy at the same premium the offering company charges other people your age. Some policies may make you wait up to six months before covering a pre-existing condition, and some may offer “discounts” for non-smokers.
If you are applying for a Medigap policy after your initial enrollment period, then in most circumstances, insurance companies are allowed to apply medical underwriting to your application, which means they may reject your application on the basis of a health condition or may charge you higher premiums even if they agree to sell you a policy. There are certain circumstances in which companies may not underwrite applications for Medigap outside of the initial open enrollment period, and some states limit or prohibit underwriting. Check with your state’s insurance department about your Medigap rights and protections.