Ann Schneider was fixing dinner in her suburban Washington, D.C., home this month when a text came from her boss: Check your email.

Ann, a 44-year-old former Nebraskan, works in a little-known unit within the Department of Homeland Security. She is a historian who builds cases against foreigners in the U.S. who are suspected of human rights abuses abroad.

Her hands shook as she read the email’s subject line: Vides is removable.

Vides is Carlos Eugenio Vides Casanova, a 77-year-old former defense minister and head of the National Guard in El Salvador. After presiding over that country’s brutal 1980s civil war, Vides moved to Florida, where he has lived comfortably for more than two decades.

But now that could change. Standing in her kitchen, Ann read the decision by the highest immigration court in the U.S., the Board of Immigration Appeals, which described in gruesome detail just why Vides should be kicked out of the U.S. ...