They'd just rotate in and out and collect money every time they pass "go". And when they get home, they're the Big Spenders and it encourages more to come.
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That's why you close the border. Send everyone home, then no one new comes in.
The EU has relatively tight borders, but they literally swim over or climb the fences or cut the wires. And they storm the borders in coordinated waves, to overwhelm the patrols.
This won't stop, until we are as poor as they are. Which is the openly-stated goal.