For more than three decades, the murder of 79-year-old Lucille Hultgren at her home in Galta has remained unsolved. It was the only cold murder in a small Sacramento community.

But now a DNA match on the victim’s nail scrapes has identified Hultgren’s killer, a sex offender who lived under a bridge on Highway 99 until his death in 2011, authorities said Tuesday.

“Nails were the key to resolving this case,” Sacramento County Attorney Anne Marie Schubert said during a news conference with Galt Police.

Haltgren was found dead in her home on May 23, 1988 by two friends who came to check on her after she missed the church, Galta Police Chief Brian Kalinowski said. He said she was strangled, stabbed and sexually assaulted.

Coroner believed the murder happened about two to five days before her body was found.

Hultgren was an active member of her church and the mother of two adult sons, one of whom died.

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The murder happened shortly after her husband’s death, and the last time one of her sons saw her alive was on Mother’s Day, Schubert said.

“She lived a modest life, by all accounts,” she said. “Her church and her faith were important to her.”

Authorities have identified Hultgren’s killer as Terry Leroy Bramble. He was a longtime resident of Galta who had never been on police radar until his death from natural causes. But his DNA was in the material on the sexual assault case in San Joaquin County, about which authorities hope to learn more.

Advances in DNA evidence analysis over the years have reached a point where a previously required sample size of a quarter could now be “less than a billionth of the size of a Sweet’N Low package,” Schubert said.

Police are now looking to other jurisdictions to find out if they have anything to do with other cold cases in the region.

Schubert said Hultgren’s body was a “silent witness” who uncovered her killer, although his motives are still unknown.

Schubert said the victim’s son would like the suspect to be still alive so he can face justice.

“I also want this man to be still alive so that we can prosecute him and put him in jail,” she said. “But sometimes justice leads us wrong.”