She cannot, no, but he can, especially with his daughter. He is a citizen, so he can apply, and his daughter is a citizen too. She needs to get an immigration lawyer and apply for an adjustment of status with an alien relative petition. There is a new law that could mean she would only need to leave the country for about two weeks for a consular adjustment. They need to talk to an immigration attorney. But he needs to be able to support her first.
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Food stamp is a state program and I have yet to see a state which allowed people without valid immigrant status to apply. Even LPRs are not eligible in most circumstances.
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