You will get a COBRA letter from your company that should detail the end date of coverage and deadlines for requesting continued coverage on your employee health plan and for sending payment for that coverage. You should have 45 days (I think) to send notice that you wish to continue coverage and longer to actually send the payment. So, it may cost to extend the coverage (COBRA is not cheap, you pay 102% of the full premium) but if something catastrophic happened, you would be able to retroactively get coverage. If noting catastrophic happens, you can also negotiate cash discounts to pay your providers for service until new coverage starts.