The short answer is you can get a continuation of your same health plan for a certain period of time, but you have to pay more because your employer isn't subsidizing your premiums. Generally this extension lasts for 18 months, though if you qualify for disability it can go for 29 months. And you do have to pay the full price for the plan because your employer is no longer providing it for you, though you may get government assistance.
I've gone through this; you should be aware that COBRA is a retroactive continuation of your coverage, from the day you leave your job, but it's not actually continuous. It can take weeks for the paperwork to go through, and during that time you effectively have no coverage. I found this out because I was scheduled for a surgery the week after leaving my job, and while checking in the hospital told me they couldn't verify my insurance. I was delayed about an hour while trying to convince them that I'd applied for (and paid for) COBRA already, and that I was, or would be, covered for the surgery that day. Eventually the department head allowed me to be checked in, but I'd gotten lucky.
The short answer is you can get a continuation of your same health plan for a certain period of time, but you have to pay more because your employer isn't subsidizing your premiums. Generally this extension lasts for 18 months, though if you qualify for disability it can go for 29 months. And you do have to pay the full price for the plan because your employer is no longer providing it for you, though you may get government assistance.
Also relevant is the Family and Medical Leave Act. Also, if you're unable to do your job due to a medical issue you may qualify for https://en.wikipedia.org/wiki/Social_Security_Disability_Ins... , along with Medicare. And there's regular disability insurance: https://en.wikipedia.org/wiki/Disability_insurance