Not all employers are required to provide COBRA benefits. Government employers, and employers with an average of less than 20 employees for the past calendar year, are not required to provide COBRA benefits. Also, an employer which completely terminates its healthcare plan (usually when the employer goes out of business or is purchased by another company) is not required to provide COBRA benefits. I have provided a link, below, to the Department of Labor's web page on COBRA eligibility. Hopefully, it will assist you in evaluating your COBRA rights.
If your former employer meets one of these exemption criteria, you may not be entitled to COBRA benefits. If your employer does not fit one of these exemptions, you may have a claim under the Employee Retirement Income Security Act (“ERISA”) for COBRA coverage and, possibly, statutory reporting and disclosure violations. This is an extraordinarily complex area of the law. If, after considering the information in the DOL's web page, you believe you have a claim for COBRA benefits, you should consult an experienced ERISA attorney.
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As the other responder said, not everyone has to give COBRA. Since they claim they sent you a COBRA notice, I assume they must provide COBRA. The law requires them to send it to your last known address. If you moved, you have to give them the new address. If they did not give you COBRA notices, you still have a right to elect COBRA coverage retroactive to August 2012 (if you were terminated on July 1, 2012, you probably lost coverage on July 31, 2012, which is your COBRA notice date). You will, however, have to pay the retroactive premiums back to August of 2012. If you really need the coverage, complete the forms and send them back. You will have to pay the full cost (which is always much higher than the amount you were paying as an employee) which can be a big number after a year. If you do need the coverage, the premium cost may not deter you from getting the coverage.