It’s a form for immigrants, not undocumented migrants. You do know people can be a legal immigrant right?

From the pdf:

1. Do I have to be a U.S. citizen to apply for public and subsidized housing? No, you do not have to be a United States citizen to apply for public or subsidized housing. Lawful permanent residents and many other immigrants may apply for all types of government housing. If your entire family is undocumented, you will not be eligible for certain federal programs. In addition, for certain federal housing programs, if some but not all of your household members are citizens or have certain types of recognized immigration status, your portion of the rent will be higher than it otherwise would be. This may result in a rent that you cannot afford and make it unwise for you to apply for those programs. See Questions 9 and 10.