Question about insurance after COBRA!

[actuarialStudent1234]

I have a question about health insurance. Not sure if it fits in this forum, but thought I would give it a shot!

I have a family friend that had an ok job - not great, but it paid the bills, and he was able to take care of himself. He is single, so not much responsiblity. Unfortunately, recently, he developed brain lymphoma, which is a type of cancer that is considered terminal. He has been hospitalized for the last couple of weeks, and is on STD at work. Sadly, in a few weeks, he will be terminated since he has not been able to go back to work, in which case COBRA kicks in for 6 months. His family is wondering a lot about what happens after that, and they came to me as an actuary, assuming I would know the answer (I work for a life insurance company, but that's besides the point). So I thought I would post here and see what the "experts" thought about this, and what options were available to him:

Some of the questions were:
1) After COBRA, can he just continue with the insurance company that he has, but pay the full premiums, OR
2) Does he have to shop for new insurance? And will this be a problem, since he is technically uninsurable?

I have no idea how it works, so any help would be appreciated.

Thanks!