One of the big problems with our current health insurance system is that health insurance is often tied to employment. This means that if you lose your job, you also lose your health insurance. It also means that if your employer cancels the health insurance for your company, you can lose your coverage due to no fault of your own.
To answer the question in the title: an employer can cancel the health insurance for its employees. This can affect not only the current employees, but also the former employees who are currently have their health insurance through COBRA. (COBRA is a federal law. It is not a federal program. The insurance you have on COBRA is the same group health insurance available current employees of your old job.)
COBRA automatically terminates when the employer no longer offers group health insurance to the employees who currently work for them. For this reason a private, non group family or individual health insurance policy can provide you with more security. (Your insurance benefits may be tied to a state or region, but otherwise will likely be something you can keep so long as you pay your monthly premiums.
I have occasionally heard stories from clients who left their jobs and have had their COBRA cancelled for nonpayment even though they paid their premiums to their former employer. The employers took their money and failed to pay their premiums on time.
Companies that are struggling to survive often drop the health insurance offered to their employees. Sometimes they are unable to pay premiums on time this can have the same impact on their employees as an intentional cancellation. COBRA can be a bad choice if your employer is struggling to stay in business.
(COBRA is a temporary solution. In most situations a former employee can only keep this coverage for a year and a half. Because of this I advise most people to purchase a non-group health insurance policy that they can cancel any month but that they can choose to keep until they are 65 and eligible for Medicare. There is no guarantee that they will still be healthy when their COBRA eligibility ends.)
If your employer fails to pay the required monthly premium for your policy, the insurance company isn’t likely to reinstate your policy. If you have paid your premium to your employer, and they didn’t pay the premium to the insurer, they have probably broken the law. However, the insurance company won’t care if what your employer did was legal or not. They may not care if the premium was paid, but paid two days late.
Since an employer can cancel your health insurance and leave you with no coverage. You might be caught holding the bag for the cost of your medical care. You may be better served by purchasing your insurance benefits on a non-group basis. This way you are in charge of whether you stay covered or not. These policies are often less expensive than group policies and can offer more security and portability.