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By February 2017, Maisha Sudbeck had made peace with the idea she would never get justice. It had been five years since she was raped in Tucson by a man she had met online. The police had brushed the case off as a he-said-she-said standoff. For years, her rape evidence kit had sat untested. With two children and a new marriage, she had moved on with her life.

Then a detective knocked on her door.

The detective said a grant from the Manhattan district attorney’s office had helped the Tucson authorities clear a backlog of untested rape kits, which preserve the DNA evidence left by an attacker. After five years, Ms. Sudbeck’s kit had finally been tested, the detective said. And the police had found a match in a database of people with criminal records: a man named Nathan Loebe.

“My chapter was reopened,” Ms. Sudbeck said. “Having my kit finally tested was a catalyst for hope.”

In February, Mr. Loebe was convicted of sexually assaulting Ms. Sudbeck and six other women. Ms. Sudbeck testified against him at trial.