...Cisco will debit my account for this insurance for December. Consequently, there is no consideration for the insurance, AND Cisco is going to pick my pocket for this lack of coverage.
What do you mean Cisco will debit your account for this insurance (COBRA) for Dec?
Cisco has nothing to do with COBRA. They provided your info to a third-party COBRA insurance provider to notify of your eligibility. They provided you with a lump sum amount equal to 4 months of your eligible COBRA benefits costs grossed up to cover taxes.
It's on you to read the paperwork sent to you by the COBRA benefits administrator, on you to enroll (if you elect to do so), and you have a limited time frame to do so, which is spelled out clearly in the paperwork mailed to you. Once enrolled, and your first payment is received, your COBRA benefits are retroactively enabled back to the last day of employment/benefits coverage with Cisco. It is your responsibility to make your COBRA payments on time, before the due date, not Cisco's. If you make a payment late, your COBRA entitlement/coverage ends and you cannot restart it. This is also made abundantly clear in the paperwork the COBRA benefits administrator sent to you.
COBRA works the same no matter who the employer is. The only thing that varies from company to company is whether or not:
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They cover your benefits until the end of the month you are terminated in, or if they end at midnight of your last day of employment.
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They provide you any money to cover some or all of your COBRA benefits and for how long. Cisco is the only company I've left who's paid for the first several months of COBRA coverage. It was 6 mo coverage when I was LR'd.
All employees eligible for an employer benefits plan, upon termination, are eligible for up to 18 months of COBRA coverage, and in some situations, it can be extended for an additional 18 mo, but you'd have to search the Internet for what those situations are.
Not to sound heartless, but it sounds like Cisco LR'd the right person in this case. Far too often, it's a hard-working, capable person who knows how to read. Hopefully you've learned your lesson about how COBRA works this time, and you're able to enroll in the normal healthcare market place ASAP or get a job w/ an employer who has a benefits plan that's effective on day one. Good luck.