Air carrier pilot reported the left engine lost oil during cruise and stopped operating. The flight crew shut down the engine; returned to the departure airport; and landed safely.

Narrative

When reaching cruise altitude of 5;000 feet I reduced the RPM setting from climb at 2300RPM to cruise setting of 2100RPM. At 2100RPM I noticed the power percentage was surging 12-15% so I increased the RPM 50; there was no change; then I increased the RPM 100 to be at 2200RPM; at this time I saw the Left engine light come on; I looked out the window at the left engine and saw what looked like oil draining out of the left engine exhaust pipe. I informed the PIC of this so we decided as a crew to return to ZZZ with mechanical issues. The PIC advised ATC and they began to give us vectors to return to land at ZZZ. While making the left hand turn the airplane began to alert us on alerting messages for LH low fuel pressure; LH low fuel quantity (the airplane had over 50 gal in the left tank); LH low fuel pressure; LH high oil temperature; LH high Turbine Inlet Temperature (TIT) temperature; LH high CHT temperature; LH high EGT temperature. As we started to get all of these alerting messages the PIC notified ATC that we were [requesting priority handling]. About 30 seconds later the left engine lost power and was at 600RPM; at this point to take precaution of engine fire and more severe damage we determined to shut down the left engine. I performed the immediate action items and maintained directional control of the airplane until the PIC was ready to take control of the airplane and navigate. After passing the controls to the PIC we performed the engine securing checklist in the QRH and began to brief and follow the checklist for single engine approach. I alerted Operations on the radio that we were now single engine on the final approach inbound to land. When switching to Tower I alerted tower we were single engine with oil spraying everywhere and to please have fire trucks ready to meet us in case of a possible fire. The PIC landed the plane on Runway XX safely and we exited the runway and were met by the rescue team.