Leo Garcia wasn’t the kind of immigrant that most countries would covet. There was still the mystery of the missing girl who’d gone hiking with him, and although he never served more than overnight jail time including the sentence (then) Judge Duncan Bon jorni gave him Leo had a record of numerous arrests in the Northwest. Most of them stemmed from fights where he’d physically hurt people or destroyed property.

He was required to present many documents to validate statements he’d given Costa Rican officials. He scrambled to get his birth certificate and proof of his place of birth in Junction City, Oregon, and he filled out a number of...