Cosby was last seen at approximately 6:00 a.m. on June 2, 1998 in Sweetwater, Texas. He walked away from his lakeside cabin while his family members were asleep, leaving the front door open. Witnesses told authorities that he was walking along north a road off Interstate 20, away from Sweetwater, on the morning of his disappearance. Cosby has never been heard from again. An extensive search produced no clues as to his whereabouts.

Cosby was employed as a shipyard worker in California for many years before returning to his hometown of Sweetwater in the 1980s. His relatives canvassed the area near the shipyard after his disappearance, hoping to locate evidence as to his fate. The business has since ceased operations. Investigators believe that Cosby may have received a ride from a passing motorist who did not realize Cosby was a missing person. He may have attempted to travel to the west coast.

Cosby's wife said that her husband complained of discomfort due to gout in his left foot during the day prior to his disappearance. The pain did not affect his walking abilities. Cosby is described as an independent person. He began suffering from dementia after suffering a stroke in 1997. Cosby's case remains unsolved.