I think the vast vast majority would continue to work hard. But leachers do exist, and given the opportunity, some will. The thing is the ones that are here illegally are already self selected as ones willing to work without social supports.

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>Leechers exist among natives too. Any particular reason to believe that it’s worse with the immigrants?

No in fact I've stated the opposite. The incentive structure for immigrants self selects the illegal ones as ones willing to work without social support, because it isn't offered to them. The legal immigrants, unless sponsored by family/spouse, generally have high education or wealth requirements than our average populace thus they're less likely to use benefits.

In fact I think my country could look at the incentive structure that has made the illegal immigrant in my country so hard working, and think about how we can apply to making our own citizenry more independent and less dependent on public benefits.