In February 1980, a townhouse at 695 Sackett Street burned to the ground, and the third-floor tenants — Elizabeth Kinsey, 27, and her five children — were killed. The townhouse’s owner, Hannah Quick, told the police at the time that it had been arson and that she had heard the three defendants inside the townhouse just before the fire and then had seen them walk out. Ms. Quick, a drug dealer, said she had been feuding with one or two of the men over drugs. All of the men were convicted at a trial in 1981.

But years later, as she was dying, Ms. Quick told her daughter that she had lied about the men’s involvement in the fire. The case found its way to the Conviction Review Unit, whose leader, Mark J. Hale, said he had no idea how the case had proceeded to trial in the first place. In an interview conducted when the men were exonerated, Mr. Hale said that Ms. Quick’s motives to lie might have included liability for the fire and an insurance payment she received.

Although a fire marshal testified at the men’s trial that he had found evidence of arson, Mr. Hale said evolving fire science disproved the 1980 analysis. Reports by experts that were filed by Mr. Villalobos’s lawyer and the district attorney’s office showed that despite the initial testimony, there was no evidence of arson and the fire was most likely an accident.

“It’s a significant settlement,” Joel Rudin, Mr. Vasquez’s lawyer, said. “This is a case where the system completely failed these men.”