Cobra insurance in a stepping stone to hold you while you are no longer getting regular inurance from your job. When you go on Cobra, the employer no longer covers any potion of your insurance, so it can be rather expensive.
The Cobra can last from 18 months to 36 months depending on the employer. In some rare cases and circumstances it may be extended, but that would be up to the employer and insurance company.
The Cobra affords you the opportunity to get other heath insurance. You may check with the company that handles to Cobra and see if you can convert to a personal policy or family policy from the same insurance.
This site gives some explanation about Cobra insurance and how it works: http://www.cobrainsurance.com/COBRA_FAQ.htm
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You can check if he had the Cancer when he was originally covered by the insurance, they may be responsible for continued coverage.
My husband had a similar situation with a Stroke and the company was forced to continue coverage, since they had covered him. This may come under a Catastrophic illness clause in the insurance policy. http://www.investopedia.com/terms/c/catastrophic-illness-insurance.asp#axzz21s5ohctM
This is very tough, because most insurances will not cover pre existing conditions. In this circumstance, I would have him apply for Social Security Disability immediately. Since he has Cancer, he should be approved quite rapidly and be eligible for Medicaide/SSA or some State subsidized health care until Medicare can kick in.
With the Government there is a Pre Existing Insurance but you have to be without insurance for 6 months to get coverage and also be turned down for insurance.