Not to make it out to be some paradise, but illegal immigration isn't a crime in Argentina or Brazil. Argentina doesn't enforce it, and in fact I have read court cases of people criminals arriving illegally with fake passport and granted citizenship.

If you are illegal, you can literally show up fresh off of jet and on day one in .ar, file a court case for citizenship, have a lawyer run down the clock for a few years (by constitution in argentina illegal residence and subsistence for a few years = citizenship), and all the meanwhile they are legally barred from deporting you.