* Hope your employer is compassionate and keeps you on their plan. I have no data on this, but anecdotally it is surprisingly common. Companies can be heartless when dealing with large groups of employees, but it is much harder to rip away Karen from accounting's health insurance as she is going through chemo.
* Hope your spouse (or parents if you are young enough) has insurance and they can add you to their plan.
* Buy in to your current insurance plan through various government programs (COBRA is one program that a lot of other comments are mentioning) . I don't have all the details on how this changed after Obamacare, but there were generally limits on how long you could do this and the costs were much higher than what your plan previously cost you and your employer.
* Buy a new insurance plan on the open market. This would have been obscenely expensive for someone with cancer before Obamacare's preexisting condition protections, but even with those reforms it still is a huge expense.
* Pay for your medical care out of pocket, which in the case of cancer will almost certainly result in you going bankrupt. Depending on where you get your statistics, there is something like 500,000 - 1 million bankruptcies in the US a year that are related to medical expenses.
