Princeton University sociologist Douglas S. Massey reports that 62 percent of illegal immigrants pay income taxes (via withholding) and 66 percent contribute to Social SecurityEven for illegals who pretend to be legal, do you think they are honest about the number of dependents when they fill out their w-2's?
Payroll taxes are not dependent on dependents.
Furthermore, people using a fake SS number will seldom file a tax return. That money just accumulates there, and nobody claims it.
I believe you can decrease your withholding by increasing the number of dependents claimed on your W-4.