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Immigrants "qualified" to receive benefits:
Lawful permanent residents, or LPRs (persons with green cards).
Refugees, persons granted asylum or withholding of deportation/removal, and conditional entrants.
Persons granted parole by the Department of Homeland Security (DHS) for a period of at least one year.
Cuban and Haitian entrants.
Certain abused immigrants, their children, and/or their parents.[5]
Certain victims of trafficking.[6]
All other immigrants, including undocumented immigrants as well as many persons lawfully present in the U.S., are considered “not qualified.”

Exceptions:

The law includes important exceptions for certain types of services. Regardless of their status, “not qualified” immigrants remained eligible for emergency Medicaid [13] if they are otherwise eligible for their state’s Medicaid program.[14] The law does not restrict access to public health programs providing immunizations and/or treatment of communicable disease symptoms (whether or not those symptoms are caused by such a disease). School breakfast and lunch programs remain open to all children regardless of immigration status, and every state has opted to provide access to the Special Supplemental Nutrition Program for Women, Infants and Children (WIC).[15] Short-term noncash emergency disaster assistance remains available without regard to immigration status. Also exempted from the restrictions are other in-kind services necessary to protect life or safety, as long as no individual or household income qualification is required. In January 2001, the U.S. attorney general published a final order specifying the types of benefits that meet these criteria. The attorney general’s list includes child and adult protective services; programs addressing weather emergencies and homelessness; shelters, soup kitchens, and meals-on-wheels; medical, public health, and mental health services necessary to protect life or safety; disability or substance abuse services necessary to protect life or safety; and programs to protect the life or safety of workers, children and youths, or community residents.[16]

In many cases, states do not have to check status:
Verification Rules

When a federal agency designates a program as a federal public benefit foreclosed to “not qualified” immigrants, the law requires the state or local agency to verify the immigration and citizenship status of all applicants. However, many federal agencies have not specified which of their programs provide federal public benefits. Until they do so, state and local agencies are not obligated to verify immigration status. Also, under an important exception contained in the 1996 immigration law, nonprofit charitable organizations are not required to “determine, verify, or otherwise require proof of eligibility of any applicant for such benefits.” This exception relates specifically to the immigrant benefits restrictions in the 1996 laws.[17]https://www.nilc.org/overview-immeligfedprograms.html