Border jumpers isn't an issue though. They either need a good reason, such as their kids not being able to get the treatment they require in their home country, or be a Swedish citizen. There's also a kind of "Green card", which requires them to do some tests and be "accepted" in order for them to get any care at all.
Getting that isn't exactly "easy", though. So we don't need to worry about border jumpers all that much. Hell, don't usually let people that only seek free health care to actually get it, unless its their kids that require it, and they can't get it in their home country.
Most of the time, to actually get entrance, it requires their country to be in a state of need, or that they can't by any means return to their country of origin by any means. Like, as an example, they are in danger of getting murdered by their husband and family, or the country being in a state of war which would endanger the person in question. And even then they might not get a permanent green card.