Air carrier flight crew taxies off end of inactive runway while taxiing to gate after night landing.

Narrative

Made a normal approach and landing on Runway XX. I was the pilot flying and did a normal transfer of control of aircraft to the Captain. Captain exited at Runway YY and we were told by Tower to exit Runway XX at Taxiway 'A' and a right on Taxiway 'B' to our gate. After performing my after landing flows I was observing the taxi in and noticed the runway environment was not lit like normal. I started to look for the 'A' taxiway on the left side of the runway but could not see it from where I was sitting. I looked in front of us and noticed we were heading for the overrun on the dept end of Runway YY. I yelled stop or brakes at this time but we were unable to stop the aircraft on the pavement and went out into the overrun. The Captain tried to get the aircraft back onto the 'A' taxiway by turning the aircraft 90 degrees but we sank into the deep sand and came to a stop on the edge of 'A.' We informed Tower that we were stuck in the overrun and to roll men and equipment to the scene. We informed the passengers to remain seated along with the Flight Attendants and got a set of airstairs and busses to transport all to the terminal. We had the aircraft unloaded and the flight crew met with an FAA rep and exchanged info. They called it an occurrence since no one was injured and there appeared to be no aircraft damage; they released the aircraft and the flight crew and we proceeded to operations where we waited for drug and alcohol testing and we were then released to our hotel for the remainder of the night. Dark and lights were not on marking the end of the runway and speed of taxiing aircraft all combined to suck us into the big hole. Could not tell where the 'A' turn off was and could not see the 'A' sign or the end of the runway. Captain should not have chosen Runway YY to taxi in on unless he was very familiar with the airport layout.Supplemental information from ACN 784240: This occurred on the first day of the trip; last leg. The flight departed CLT on time. The First Officer was flying the aircraft; the flight was uneventful through landing. After landing at ZZZ Runway XX; control of the aircraft was transferred to the Captain. Turning off Runway XX at the intersection of Runway XX; Ground Control instructed us to taxi to the ramp via XX; Taxiway A; to B; to the ramp. It was dark at the time with no runway lighting except for edge lighting. As we slowed our taxi speed to turn off at A; it was noticed that there was no lighting at the end of the runway. Slowed further; but still could not identify the end of the runway until I actually taxied off the end of the runway. After assessing the situation; I believed that I could taxi the aircraft back to the Taxiway A or B without damaging the aircraft or injuring our crew or passengers. However; after a short distance the aircraft became stuck on the infield. The engines were shut down; Ground was notified of out situation and ZZZ operations were called to help deplane our passengers and their bags. After passengers were taken off aircraft we noticed that the runway end lighting had been turned back on. Crew stayed with the aircraft until the FAA rep showed up and released the crew and aircraft. They stated that they considered the incident as an occurrence. The Flight Attendants went to the hotel. The Captain and First Officer at ZZZ operations until a breathalyzer and urine test were administered. Long Day; dark conditions; no runway lighting; especially end of runway lighting turned off.