A hydraulic system is disclosed. The hydraulic system may have an over-center, variable-displacement pump, an actuator, and first and second passages that create a closed-loop circuit. The hydraulic system may also have first and second check valves disposed in the first and second passages, respectively, to allow flow only from the pump to the actuator. The hydraulic system may further have a first bypass line connecting the first passage at a location between the actuator and the first check valve to the first passage at a location between the first check valve and the pump, and a second bypass line connecting the second passage at a location between the actuator and the second check valve to the second passage at a location between the second check valve and the pump. The hydraulic system may additionally have a valve configured to control flow through the first and second bypass lines.