Jones and another 35-year-old inmate were found unresponsive in their housing unit about 8 p.m. Monday.
After life-saving measures were provided, including CPR and naloxone administration, correctional officers and medical staff had the men taken to Bayhealth Hospital, Kent Campus.
Jones, who was admitted in critical condition, died about 5:30 p.m. Wednesday. The second inmate, who was admitted in stable condition, fully recovered and has been returned to the Smyrna-area facility.
Jones' body was turned over to the state Division of Forensic Science to determine the cause of death. A death investigation is being conducted by Delaware State Police and is pending at this time, Shavack said.