The Trump administration will make it much more difficult for immigrants to come to the United States or remain in the country if they use or are likely to use housing vouchers, food subsidies and other “non-cash” forms of public assistance, under a new proposal announced Saturday by the Department of Homeland Security.

U.S. immigration laws have long contained provisions limiting foreigners who are likely to be dependent on financial aid and therefore a “public charge.” But the proposed changes amount to a broad expansion of the government’s ability to deny visas or residency to immigrants if they or members of their household benefit from programs like Medicaid Part D, the Supplemental Nutrition Assistance Program (SNAP) or Section 8 housing vouchers.

“Under long-standing federal law, those seeking to immigrate to the United States must show they can support themselves financially,” said DHS Secretary Kirstjen Nielsen said, in a statement, adding that the proposed changes would “promote immigrant self-sufficiency and protect finite resources by ensuring that they are not likely to become burdens on American taxpayers.”