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Even without that, there's a lot of issues about giving them welfare. We could allow them entry as second-class citizens who have no minimum wage or access to welfare but still need to pay taxes. We'll avoid having to give them welfare, but we'll need to admit that we have second-class citizens, which is something we pretend to be against.
It also means that the people who are currently working at minimum wage jobs are likely to lose their jobs to the cheaper competition.