Dunbar worked his way into a change-of-pace role out of the Dallas backfield as an undrafted free agent out of North Texas three years ago. He had 362 all-purpose yards last season, topped by 217 yards receiving.
The 25-year-old Dunbar has a chance for an expanded role with NFL rushing champion DeMarco Murray's departure to Philadelphia in free agency.
Jones has been with the Cowboys four seasons, the past two as the full-time punter. He had a career-best 45.4-yard average last season. His career net average is 39.5 yards.
Dunbar and Jones were the last of Dallas' restricted free agents.