If it is the case it seems out of context to refer to this severance benefit as COBRA as it is my understanding this program has been specifically designed by Congress to force employers to offer the "opportunity" for the separated employees to get health insurance at full cost (without the employer subsidy).
Since the Affordable Care Act, it seems to be cheaper to forego COBRA benefit and enroll in one of the offered options. Lost of job let you do so outside of the official enrolment period.
