If it was up to me, any one entering an ER with no means to pay would have their immigration status verified, this can even be done after life saving emergency care is provided. Anyone found to be here illegally would get nothing more than this such care, and then be subsequently deported.
Bet we'd only need to do that once.
France doesn't let anyone in without pre-arranged medical insurance. That's one of the reasons all those Africans and other illegals were over there at the Chunnel trying to hitch a ride to UK where they just give it away to anyone.
We could treat them and send the bill to the country from whence they came.