Some 350,000 travelers arrive by air in the United States each day. From Asia, South America and Africa, they come mostly with visas allowing them to tour, study, do business or attend a conference for an authorized period of time. But when they stay beyond when their visas expire, some of them fall into the same illegal status often associated with migrants showing up at the border.

Nearly half of the estimated 11 million undocumented immigrants now in the country did not trek through the desert or wade across the Rio Grande to enter the country; they flew in with a visa, passed inspection at the airport — and stayed.

Of the roughly 3.5 million undocumented immigrants who entered the country between 2010 and 2017, 65 percent arrived with full permission stamped into their passports, according to new figures compiled by the Center for Migration Studies, a nonpartisan think tank. During that period, more overstayers arrived from India than from any other country.