One of the largest healthcare networks in the region is set to end its relationship with a health insurer in June, if new terms aren't reached. Kettering Health Network and Kettering Physician Network's contract with Cigna (NYSE: CI) will be expiring June 14. If the parties cannot reach new terms by this date, Kettering Health Network hospitals and Kettering Physician Network providers will be considered "out of network" with all Cigna plans beginning June 15, according to a letter from the health…