William and Theresa Reilly were biking on a leafy trail north of Detroit when their son, Billy, sent a text from his trip to Russia. The 28-year-old man had never lived away from home, and the Reillys fretted over his safe return.

Billy Reilly had yet to find a career, but his foreign-language and computer skills led to part-time work in counterterrorism for the Federal Bureau of Investigation in Detroit. He was one of the bureau’s army of confidential sources, and the Reillys didn’t know if his trip was somehow connected....