That is one of the difficult things about just "shutting down" medical services...
When an ambulance is called, those paramedics don't have the mindset, nor should they, to be INS agents and ask for proof of citizenship before treating someone.
Unless there was a law that would let the hospital people call the authorities, if they have no proof, after they get THERE, the people will still get treated.
Our country just does NOT refuse medical help to people, regardless of legal status.
Perhaps, though, like empowering the local police departments to arrest illegals, they should empower hospitals and clinics to at least call ICE..and maybe even the paramedics if they just treat someone, but don't transport to a hospital.
That is what I think should be done, just treat and call in immigration.... but there is another issue higher up the chain-- when these people apply for Medicaid I've been wondering -- does the Social Worker not check if the person is a legal immigrant? So many cannot speak English (the doctor I work for has to employ people who can translate for him) that I would think it's a red flag to the Social Workers... and they have to provide an address when they apply as well...