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For the more than 797,000 others whose cases were not reviewed further, DHS officials said their overstay status was noted in electronic files in case any of them commit crimes in the future or otherwise become a priority to be deported.

Visa overstays long have been a concern of lawmakers and law enforcement. Some estimates suggest that as many as half of the country’s estimated 11 million illegal immigrants have overstayed visas.

But finding illegal immigrants who, like Mr. El Khalifi, came to the United States before biometric data was collected and records were computerized around 2004 — and who overstayed visas but haven’t committed a crime — can be difficult, if not impossible.

“It’s very difficult to find those individuals, and those individuals aren’t priorities until they commit a crime,” said Julie Myers Wood, who was head of ICE from 2006 to 2008.

James Ziglar, who was head of the old Immigration and Naturalization Service from 2001 until it was folded into DHS in 2002, said immigration authorities made efforts to locate immigrants thought to be a threat to national security after the Sept. 11 terrorist attacks. But simply having overstayed a visa wouldn’t have made illegal immigrants such as Mr. El Khalifi a priority.

“We were certainly focused on trying to find bad people and connecting the dots with the Department of State and their visa records,” Mr. Ziglar said. “I doubt very seriously (Mr. El Khalifi) would have come up on the radar. He might have if you kept drilling down further and further just because of where he was from. But he would not have been, I think, an earlier target, just because there were more suspicious types.”

Associated Press writer Eric Tucker contributed to this report.