I'm no attorney, but even the IRS can't leave you homeless and they have much greater powers than any hospital I know. In some states, maybe all as I'm pretty sure it's a federal issue, when a nursing home takes someone in, the patient must assign their assets over to the nursing home to offset the cost of care, or they probably won't take them. The home cannot be transferred to avoid it as they can go back I believe 5 years to get it.
The nursing home cannot force the sale of the home because there is an underlying right of the patient to return to the home should they become competent enough to care for their own needs again. Then they will just have an outstanding bill. If the patient dies while in the nursing home, they will sell the assets to pay the accrued bill. While it seems harsh, a nursing home is actually taking a risk that someone's assets will cover the cost of their care for an extended period of time. It's not unusual for someone to be in for 5, 10, or more years.
As to a regular hospital taking someone's home in lieu of a debt, I suspect if you're making payments, however small, they'd have a hard time doing anything. They would have to file suite and suing someone out of their home for unpaid medical bills is really bad PR.
I could be wrong about some of this stuff, but I suspect a quick consult from one of the attorney types on CPF, as I know we have them, will shed a little more light on the issue.