OK, I just dug this up. This is the exact way illegal immigrants can get benefits. It's similar to what I thought but also a little different, and I guess some can get benefits. I don't know
First, fraud and administrative errors allow some number of illegal immigrants to collect benefits.
21 Second, illegal immigrants can live with adult green card holders or U.S. citizens who can use these programs. Third, in the case of Medicaid, pregnant women illegally in the country can sometimes be enrolled in the program. Fourth, there is the Emergency Medicaid program that covers predominately illegal immigrants.
22 Finally, it must be remembered that illegal immigrant households without children accessing these programs comprise only 14 percent of all illegal households receiving welfare benefits.