How about the entirety of the US medicaid program? If you literally have no income you get free healthcare, even if you have limited income you may qualify for Medicaid or a heavily discounted marketplace plan.
Based on that article, the programs vary widely by state including eligibility standards and rates of reimbursement.
> As of 2013, Medicaid is a program intended for those with low income, but a low income is not the only requirement to enroll in the program. Eligibility is categorical—that is, to enroll one must be a member of a category defined by statute; some of these categories are: low-income children below a certain wage, pregnant women, parents of Medicaid-eligible children who meet certain income requirements, low-income disabled people who receive Supplemental Security Income (SSI) and/or Social Security Disability (SSD), and low-income seniors 65 and older.
This makes it seem like it's not just "low income", but also membership in one of those other categories.
I also didn't see anything on the page that indicated what share of expenses were covered by medicaid, but perhaps I missed it.
Though I suspect it's a lot more complicated than calling them up, telling them you've decided to take a gap year, and asking for your insurance card. It also wouldn't surprise me, never having looked into it, if the coverage is US only.
There's an online form where you upload your info, they verify your income level (duration does not matter), and that's it (at least in NY). I don't think any government healthcare programs cover care outside that government's country, do they? I suppose the EU ones cover care in other EU countries but that's the only case I can think of.
https://en.m.wikipedia.org/wiki/Medicaid