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Are you implying that other people have some sort of obligation to take in random people from outside of their countries? That's fine if you're immigrating for work, but a lot of the immigrants that come here on a visa vote for bigger government and a generous welfare state funded by the citizens' taxes. It would be even better if you were to encourage people in other nations to not participate in local elections since it is very evident that politicians cause 90% of the problems that they experience on a daily basis. Therefore, they would be much happier without government corruption that fuels their constant problems with immigration to other countries. As for freedom of movement, certain restrictions will have to be put in place by people who own private property in order to keep their property from getting damaged or stolen by trespassers without the need of the state. People who break the restriction will have to face the consequences. This is called the non aggression principle. The non aggression principle relies on the fact that private property owners have the full saying in who they can allow onto their property and who will not be allowed. So people who own large portions of land near the U.S/Mexico boarder, will crowdfund projects and programs that will keep their property from getting effected by people from the other side. All in all, this isn't enforced by the state because the owners of the property can can all agree to hire private security or they can all keep an eye out and defend each other to keep the neighborhood safe in case any one is breaking the NAP (Non Aggression Principle).

No, certainly not implying any individual obligation.

Immigrants who do not arrive legally are not eligible to vote or receive all forms of welfare. In fact they tend to contribute more than they extract, see here: https://www.huffingtonpost.com/entry/no-undocumented-immigrants-arent-stealing-your-benefits_us_5a144263e4b010527d6780b0

That said, these are people not numbers on a spreadsheet.