Pilot reported confusion regarding the tower operating hours. While on an instrument approach at night the tower closed and shut off the runway lights without warning the aircraft on final.

Narrative

Jacksonville Center switched us to MYR CTAF frequency and said to call them back (JAX Center) to close the flight plan upon landing. Shortly; after switching over to the CTAF frequency; the FO; PM; made a position report that we were 20NM northwest of the field descending for the RNAV (GPS) Runway 18. A seemingly confused response was received from MYR tower asking for the aircraft call sign. We again stated who we were. They asked if JAX center had sent us over and if they had cleared us for an approach to which we responded in the affirmative. Confusion or miscommunication happened between JAX Center and MYR Tower on whether the tower was actually open or not. This could have easily led to us inadvertently entering Class D airspace without good two-way with tower or a potential conflict with other aircraft in the pattern.Additionally; while outside the FAF for Runway 18; MYR tower made their standard speech that the tower and Class D airspace were closing. We did not respond to the transmission as it was an advisory call to all aircraft on frequency. While fully configured but still outside the FAF to Runway 18; MYR tower shutoff all lights at the airport and the flight deck momentarily lost visual with the airport. The PM immediately re-lit the runway environment through PCL.Confusion on the part of JAX Center on whether or not MYR Tower was open. Also; MYR Tower did not directly communicate with us that the airport would immediately go dark upon their closure. JAX Center and MYR Tower's miscommunication could have led to us inadvertently entering Class D airspace without good two-way with tower or a potential conflict with other aircraft in the pattern. Additionally; safety of flight could have been a factor if the airport/runway lights had been turned off when we were closer to the runway. MYR Tower should not turn off runway lights with aircraft on final without two-way communication and consent from said aircraft.