You may be entitled to either COBRA or retiree coverage if you stop working and have Medicare coverage.
COBRA is a federal law that gives certain employees and their dependents the right to keep their health insurance from their former employer for between 18 months and 36 months if they pay the full premium themselves. COBRA always pays after Medicare pays. If you have COBRA before you become eligible for Medicare, COBRA may terminate when you become eligible for Medicare. If you have Medicare and then become eligible for COBRA, you should be able to keep your COBRA benefits.
Retiree coverage is insurance you may get from a past job after you retire. Retiree insurance almost always pays after Medicare. That means you need to enroll in Medicare Part A and Part B so that you will have full insurance coverage. Retiree plans may help you pay your Medicare copays and deductibles. A retiree plan may also cover services that Original Medicare does not cover, such as vision or dental care.