If, in fact, they have something like that, look into a short-term policy, such as Assurant Health. We had a situation here where our company "forgot" to put someone on the policy and then wouldn't (ARRGGGHHH). So, we got the individual a short-term policy through Assurant for a very minimal cost. The details of hers was that it was the up front cost of the whole policy for a set period (like $300 or so for three months), with a $500 deductible, no copays or anything, just the $500 and once you hit the $500, everything was covered 100%. Check it out. It certainly worked for her.
Most HR professionals will go to bat for the employee. I run an HR department and I feel that the #1 priority in my job is making sure that an employee's benefits are in order and that they have no problems. When I took this position, I asked the employees, "what can I do better than my predecessor?" And the overwhelming answer was "help us!" She would just give them the carrier phone # and say handle it yourself. Now, when people have problems, they know they can come to me with bills/issues and I will get on the phone with the carrier and get it figured out. Plus, it does help to have a self-insured policy. It's more "user friendly" for lack of a better term.