If you already have Medicare but then lose your job and receive COBRA, you can have both. You’ll use your Medicare coverage first, then COBRA. That means that if you become ill, all of your medical costs will go through your Medicare coverage. Any leftover costs that you have to pay out-of-pocket may be covered by your employer coverage (COBRA). If you already have COBRA and then become eligible for Medicare, you may lose your COBRA coverage. It is always important to enroll in Medicare as soon as you become eligible. A Medicare Plan Finder agent can help you enroll.