He was placed on a gurney and taken to a medical unit, where a nurse said she thought he was faking and instructed him to “get up,” according to the investigation. A nurse and an officer removed his clothes and put him in a shower, where for at least 90 minutes he was unable to move, according to the investigation.

He was sent back to the medical unit, where the medical staff believed he was suffering from “psychosomatic paralysis” and suggested that he be placed in the video-monitored cell. He was not seen by a doctor until Oct. 25, when he was dragged on a blanket into the cell.

There, as seen on the video footage, prison staff members tossed Styrofoam containers of food near Mr. Williams, but he was unable to feed himself. He twisted his arms to dab his fingers into the water, struggling to bring drops to his mouth. Throughout the video, his legs remain motionless.

On Oct. 27, a doctor examined Mr. Williams and recommended he be taken to a hospital, but no immediate action was taken, according to the police investigation. He was discovered dead in the cell less than three hours later.

He died from complications of a broken neck and showed signs of dehydration, according to The Frontier, a local news organization.

“I can’t imagine something that was more of a nightmare,” Mr. Smolen said in an interview on Tuesday.

The family sought $51 million — $1 million for each hour in the video — but was satisfied that $10.25 million would create enough of a deterrent effect, Mr. Smolen said. Tulsa County will pay $10 million, and Stanley Glanz, a former sheriff, is responsible for an additional $250,000, Mr. Smolen said.