COBRA came into being in 1985 with the passage of the health benefits provisions in the Consolidated Omnibus Budget Reconciliation Act (COBRA). Under these provisions, voluntary or involuntary terminated employees and those who lose coverage because of reduced work hours may be able to buy group coverage for themselves and their families for a limited time period.
If you already have Medicare coverage on or before the date you became eligible for COBRA, you can take COBRA coverage along with Medicare. Medicare is primary, so you need to take Part B to avoid later penalties. If you qualify for Medicare after qualifying for COBRA the employer can terminate COBRA coverage. For more information on COBRA see the SHIIP factsheet COBRA—Continuation of Employer Group Health Insurance.