Whether you can or not depends.
Under the law, you are entitled to 12 weeks of FMLA per 12 month period. NOT per condition - per 12 month period. There are several different ways of counting the 12 month period, all of them legal.
If you had already used your 12 weeks of FMLA in the 12 month period counted as your employer counts it, then you are not entitled to any more, no matter how valid your need for additional time. There is no "extenuating circumstances" clause in the law. The employer MAY give you more time than the 12 weeks, but he is not REQUIRED to.
No notice is required before a termination. Health insurance MUST be cancelled as evidenced by the terms and conditions of the policy.
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The employer has up to 44 days to offer COBRA under the law. There isn't any requirement of pre-notification of cancellation. IF (and I do not know this to be the case, but it sounds reasonable based on the poster's description, it is legal, and it is very, very common) health insurance ends on the last day of employment, then the employer MUST term insurance on the last day of employment. They are required to follow the policy.

