A pair of Department of Homeland Security officials told the Senate Wednesday that the government does not search for most of the people who overstay their temporary visas, a day after DHS said that nearly 500,000 people were still in the U.S. after having overstayed their visas last year.

“I didn’t mean to imply that we’re actually out monitoring them,” Craig Healy, an assistant director at U.S. Immigration and Customs Enforcement, told Sen. Jeff Sessions, R-Ala., during Senate Judiciary subcommittee panel. Healy said that they review the universe of people who overstayed their visas and “prioritize” the deportation of people who went on to commit other crimes.