Medigap insurance, also known as Medicare Supplement Insurance, is a type of private insurance that helps cover the gaps in Original Medicare. While Medigap insurance cannot be denied based on pre-existing conditions during the Medigap Open Enrollment Period, there are certain situations where an insurance company can deny coverage or charge higher premiums. These situations include applying for Medigap insurance outside of the Open Enrollment Period, having a pre-existing condition and not enrolling during the Medigap Guaranteed Issue Period, or not meeting the eligibility requirements for Medigap insurance. It's important to understand the specific rules and regulations regarding Medigap insurance in your state, as they can vary. If you have questions or concerns about Medigap insurance, it's recommended to consult with a licensed insurance agent or contact your state's insurance department for more information.