Some credit cards come with automatic travel insurance, but regardless it is well worth researching before you travel. Hospital stays abroad sometimes need to be paid out-of-pocket until you are reimbursed later on.
It all depends on the circumstances, your country of origin and any extra insurance you might have taken out.
I ended up in hospital for a fairly routine operation about a decade ago and had to pay out of pocket, luckily it was in a place where they just charge you for actual cost rather than to try to balance their budget by bankrupting you so it ended up being $1500. The same thing in the US would have been a large multiple.
I mean, I have no idea what would happen if I broke my arm while overseas either. I have insurance (in the US), and assume it would get sorted out somehow, eventually, but I have no idea what my share would be. I just don't anticipate being turned away at the hospital door though.