The Lake Shore Limited runs between Chicago and New York City without crossing the Canadian border. But when it stops at Amtrak stations in western New York State, armed Border Patrol agents routinely board the train, question passengers about their citizenship and take away noncitizens who cannot produce satisfactory immigration papers.

"Are you a U.S. citizen?" agents asked one recent morning, moving through a Rochester-bound train full of dozing passengers at a station outside Buffalo. "What country were you born in?"

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