The hospital could bill the government and write off the rest. If they have insurance, then they're on the hook for whatever is left over after the insurance pays.

My HCBW and kids were visiting family out of state when my 1 year-old daughter came down with an ear infection. My wife took her to a urgent care center for treatment. Turns out that the urgent care was really a mini ER and the visit ended up costing me $2000 because it was out-of-network. I called the billing department, complained about the bill being two grand, and tried to see if we could cut a deal. They told me since I had insurance and the $2000 counted toward my deductible I had to pay the entire bill.