B737-800 First Officer reported an engine was shut down due to low oil quantity and pressure during cruise. Flight continued to destination and landed normally.

Narrative

We were operating a flight from to ZZZ; with the captain acting as PF and myself as PM. Approaching top of descent at FL210; the lower display unit automatically populated the engine indications; showing an amber low oil pressure alert and low oil quantity indicating zero. I continued in the PM role and accomplished the applicable QRH procedures for low engine oil pressure and quantity; which resulted in a precautionary engine shutdown.We continued the descent toward ZZZ; where winds were gusting in the high 30s with light snow. A diversion was considered; however; ZZZ was ultimately determined to be the safest and most suitable airport due to more favorable runway alignment and the fact that the approach had already been briefed and set up. Nearby airports reported slightly lower winds but with a greater crosswind component.During the descent; while managing a high workload environment; a brief unintended VNAV-related level-off occurred; resulting in airspeed decay. Thrust was increased on the operating engine to arrest the deceleration; and the autopilot was disconnected to expedite airspeed recovery and continue the descent. Level Change" was selected to maintain descent guidance. Subsequent level-offs required higher than expected thrust; which led to slightly slow conditions that were corrected with additional power.The aircraft landed below maximum landing weight. Despite gusty conditions; the approach; touchdown; and rollout were normal. After clearing the runway; Airport Rescue and Firefighting inspected the aircraft. Passengers were asked to remain seated during the inspection; which revealed no visible damage; smoke; or fire. The aircraft then taxied to the gate under its own power; passengers deplaned normally; and shutdown procedures were completed. The captain coordinated with Dispatch and Maintenance Control following the event.Subsequently and completely unrelated to the engine shutdown; the auto-leveler of the jet bridge malfunctioned while deplaning passengers. The jet bridge got beneath the main cabin entry door and briefly lifted the aircraft by the door. The jet bridge was lowered; disconnected; and reattached to continue deplaning. The captain wrote it up; and was in further communication with Maintenance Control and the company over potential aircraft damage. Cause: The aircraft oil had been serviced prior to departure. It was also noticed after the fact that it had been serviced twice in two consecutive flights. We had three different aircraft assignments before this aircraft; and were over an hour delayed; so failed to notice this red flag. This was also not flagged by maintenance; and may or may not have been the root cause. Company procedure is to hide the engine indications after start. The automatic population of the engine display immediately drew our attention to the oil quantity indicating zero. It is unknown whether the oil loss was sudden or gradual due to the indications being hidden; however; the automatic display feature was effective in promptly alerting us to the issue. Checking engine parameters at top of climb and subsequently every hour would be another potential mitigation strategy for recognizing an issue earlier."