Medicare with a good Medigap supplemental policy is actually pretty adequate for the vast majority of U.S. retirees. Only if you get a rare condition that Medicare flat out doesn't cover, or choose an expensive elective medical procedure, would you run up large bills.

What does happen quite often is that someone will require long term skilled care in a nursing home. Medicare only covers 100 days. Medicaid, the means tested medical coverage, will pay for long term care, but only after the beneficiary exhausts all but their last $2000 in assets (there is some protection for a primary residence, especially if there is a spouse still living there). The upshot is that a large majority of persons needing long term care end up dying with pretty much zero net worth.