Zero, obviously. People either let them lapse where possible, declare bankruptcy to get Constables off their backs, or spend years paying $50-$100/mo.
Things like this happen even to insured people. Due to a communications snafu between the doctor and the insurance company, my mom, who has "good" insurance from BigCo, is paying for her annual mammogram $50/mo now, and will be doing this for the better part of two years.
My parents paid on an ER visit I made in my late teens until I was 21 or 22 because of another such insurance oversight.
These happen all the time because that's how insurers make money. The insurance model is based explicitly on not paying out. For something that's universally utilized like health insurance, that generally means you have to deny a lot of claims to keep acceptable margins.
Homeowner's insurance works fine because most people aren't burglarized often and most peoples' homes don't burn down, so people make modest monthly payments and one claim in a lifetime more than pays for itself. Likewise, car insurance is not used too often by its patrons.
Health insurance, however, is used (at least) several times a year by almost every individual. As such, insurance is a terrible model for health care, since the entire concept behind insurance is that more people are paying for the coverage than are using it. The continued feasibility of medical insurance depends on people not getting medicine.