In most organizations, open enrollment for changing and enrolling in employee benefits plans occurs over a 30- or 60-day period of time, once a year. Open enrollment is often at the end of the calendar year, but can happen at any time of the year based on the rules created by the employer. For traditional benefits plans, I am not aware of federal or state rules that control how employers or insurance providers are to offer open enrollment. I hasten to add that I am far from being a human resources (HR) expert.
There are rules that govern open enrollment in so-called "cafeteria plans." If the employer in question offers a cafeteria plan, see ChangeOfStatus.com to learn more about the rules for cafeteria plans. So-called "qualifying events" for entering or leaving a benefit plan include birth of an employee's child, spouse's enrollment in another plan, spouse losing a job and thereby losing coverage, and so on.
I confess I am of two minds regarding your question. My first reaction is that open enrollment is typically of such a long duration that it is difficult to foresee a circumstance where a family member on leave from job would not be able to carve out an hour or so in a 30-day period to telephone the HR department and discuss the options, and then fax or mail the completed forms to the employer. Without knowing the circumstances, it strikes me that the death in the family is an excuse for failing to complete some routine paperwork by what should have been a well-known deadline. Attending a funeral is not a qualifying event.
My second reaction is that I do not know the circumstances here. Perhaps the deceased was out of the country. Perhaps the employee was involved in the treatment of the deceased, such as donating an organ. Regardless of the location of the deceased or the employee's involvement, the open enrollment deadline is completely arbitrary. The employer and employee are paying for the coverage and as such are the customers of the insurance company. The insurance company should welcome a new member of the employer's group as each new member should mean more profit for the insurance company.
Accordingly, suggest the employee contact the HR department and explain the situation to a savvy human resources person. I have no doubt that the most junior HR person will parrot, "Open enrollment is closed, open enrollment is closed." A conversation with a more senior HR person who understands that adding an employee is in the best interest of the insurance company will contact the insurance company's account representative and find a way to get the employee enrolled.
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I hope this information helps you Find. Learn & Save.