As per federal law, it is mandatory on the employers who lay off their employees , to continue coverage of health insurance plans the employees were holding at the time of termination for a period of 18 to 36 months, till the employees find another job. This extension of coverage is called COBRA and it creates a bridge between the present insurance and the next insurance, and it is incumbent on the employer to extend the benefits of insurance even after you leave the company, till the time you find another employment or an alternate insurance.
COBRA might seem to have been designed with good intention that an employee should not be deprived of his legitimate benefits immediately after leaving the company. But, it has its downside. Now that you do not have an employer to bear the 50% of your premium, you are expected to pay the entire premium amount. In the first place, you lost your job and have no income and added to that, you are expected to pay full premium? What an irony! Is it really bridging the gap, or is it removing the carpet from under your feet? So, if it is in your interest to continue paying for the COBRA and you can afford it, do so by all means. Otherwise, give it up and look for some provider whose monthly premium will not be a burden on you, even if you stay unemployed for some period, till the time you are in a position to think with clarity about your next course of action.