LOS ANGELES — At 15, in the throes of a teenage rebellion, Debbi Domingo ran away from her mother’s home in Goleta, Calif., a small town near Santa Barbara. Two weeks later, she returned home to a swarm of police cars in the cul-de-sac. Her mother and her mother’s boyfriend had been brutally murdered after being tied up and beaten so badly that detectives were initially unsure of their identities.

It was 1981 and the authorities struggled for any clues that could lead to a possible motive or suspect in the killing of her mother, Cheri Domingo, then 35, and her boyfriend Gregory Sanchez, 27. The police looked into possible drug use or unpaid debts. Officers questioned Ms. Domingo’s father for hours, chasing the possibility that he might have attacked his ex-wife.

A conclusive answer did not come until three decades later, when a major break in a very cold case led to the arrest of Joseph J. DeAngelo, 72. Law enforcement officials consider him the Golden State Killer, who is believed to have committed more than 50 rapes and 12 murders.

“This not a club anyone really wants to be a member of,” Ms. Domingo said Thursday, speaking by phone from her home in Lubbock, Tex. For her, learning that her mother’s murder was part of a series of attacks was “comforting” in an odd sense, she said. “From my perspective, when it was looked at as something totally isolated, it’s easy to feel very insignificant, like your case is easily forgotten.”