The New Republic is currently carrying an article which starts from the preposition that Democrats and Republicans alike have no intention of funding health treatment of illegal immigrants in the US: they don't pay taxes, and they're illegally in the country, so the US owes them nothing.
I have no position in this debate.
In Israel there has been a discussion recently of the problems our security forces sometimes make for ailing Palestinians who wish to be treated in Israeli hospitals (would you want to be treated in a Palestinian hospital if there was any alternative?). In a rather unusual but extreme case, a number of Gazans were refused entry into Israel last week, and now one of them has died of the cancer he hoped to be treated for. Kind of hard to see what sort of security threat he could have posed.
Here's something I wrote about this subject and others, about three and a half years ago; a version of it then appeared in the Jerusalem Post. The situation was complicated then, and is no less so now.