If the employee did not really quit, but instead was terminated, I would have several concerns.
First, if the employer had more than 50 employees within 75 miles and the employee was employed more than 1 year, there would be Family Medical Leave Act coverage, and the employee should have been offered FMLA leave instead of being terminated. Second, I would also be concerned that the employer discriminated against the employee based on a disability or failed to make reasonable accommodation.
With the COBRA paperwork, the employee typically does not receive that until 30 days after termination, but if the employee selects COBRA, the employee is covered during the 30 day wait anyway.
It is always sad to hear of terminal cancer, however, and it is understandable that someone would not want the aggravation of legal proceedings under the circumstances.
The facts provided open up many important questions. ER treatment does not in and of itself constitute a quit. The facts suggest that an employee covered by the FMLA (Family and Medical Leave Act) would rights to return to work after the absence for a serious health condition. I cannot tell from the facts if the FMLA is implicated. Similarly, the underlying condition may qualify for protection as a disability under state and federal law. Was the employee able to return to work? If you would like to discuss your facts, please contact an employment lawyer. I am happy to take your call.