When Martha Cunningham was found dead near Knoxville, Tenn., in January 1975, her body was bruised, her clothes had been pulled off and she was missing her purse.

Not long after, the police closed the case. A medical examiner’s report listed the cause of Ms. Cunningham’s death as unknown, according to David Davenport, a retired investigator for the Knox County Sheriff’s Office who later reopened the case.

Nearly half a century later, Ms. Cunningham’s family has learned what they and the police now believe is true: that Ms. Cunningham, 34, was one of scores of people killed by Samuel Little, whom the F.B.I. identified this week as the most prolific serial killer in United States history. Jessie Lane Downs, Ms. Cunningham’s sister, said she was still pained that the case was closed so quickly, all those years ago.

“The police department did not ask the family any questions or anything when this happened,” Ms. Downs said. “They could’ve settled this, and look at all the people that got killed.”