WASHINGTON — Thousands of legal residents and citizens, including 55,000 children who are in the country legally, could be displaced under a proposed rule intended to prevent undocumented immigrants from receiving federal housing assistance, according to the Department of Housing and Urban Development.

The proposal, published on Friday, would prohibit families in which at least one member is undocumented from obtaining subsidized housing, according to an analysis by HUD career officials. The administration is pushing the changes to ensure that the benefits are awarded only to verified citizens — a move that was made without the knowledge of many longtime housing officials at the department.

Current rules bar undocumented immigrants from receiving federal housing subsidies, but allow families of mixed immigration status to live in subsidized housing as long as one household member is a legal resident. The subsidies are prorated based on the number of eligible members of the family. According to the HUD analysis, more than 108,000 people receiving benefits are in a household with at least one undocumented immigrant.

Under the proposed rule, families of mixed status would no longer be permitted to live in public housing. Members who are in the country legally would be allowed to stay in their home, but the analysis found that they would be unlikely to do so: The fear of a family separation alone — and displacing one or both of a child’s parents or guardians — would have the effect of driving the entire family, including children, to vacate.