A Center Controller reported an aircraft was descended to an altitude below the Minimum IFR Altitude. The Center assumed the Approach Control airspace due to the Approach Control closing due to staffing issues and the Minimum Safe Altitude Warning was turned off.

Narrative

Aircraft X entered a 9000 ft. MIA at 8000 ft. Aircraft X was instructed to climb to 9000 ft. once the situation was recognized. No other deviations occurred afterwards. ZZZ1 handed off Aircraft X to ZZZ 21. ZZZ 21 had assumed responsibility for ZZZ2 Approach's airspace until XA00 due to staffing. Aircraft X data block showed level 8000 ft. and filed flight plan showed ZZZ3.VXX.ZZZ2..ZZZ2. The MEA on VXX is 8000 ft.; however per the LOA between ZZZ and ZZZ1; when ZZZ has assumed responsibility for ZZZ2 Approach then ZZZ2 landing aircraft will be cleared direct ZZZ2 VORTAC at 12000 ft. coming from ZZZ1. Additionally; while Aircraft X entered and was within the 9000 MIA the E-MSAW alert failed to display.Due to the non-standard configuration of ZZZ 21 controlling ZZZ2 Approach during day shift hours there was an unfamiliarity with the agreement between ZZZ and ZZZ1 for ZZZ2 landing traffic procedures. Additionally; the target position of Aircraft X initially reflected that they were on VXX leading to the assumption that Aircraft X was established safely at or above the MEA. Finally; the failure of the E-MSAW alert was the final contributing factor to the low altitude of Aircraft X. Review of procedures between ZZZ and ZZZ1 when ZZZ is controlling ZZZ2 Approach airspace. This would be helpful for all controllers to review as ZZZ2 Approach has been closed more often during the week on the day shifts which leads to new and unpracticed traffic patterns between ZZZ and ZZZ1. Change the areas where the E-MSAW alert is muted automatically for aircraft landing at ZZZ2. 20 miles south of the airport is too far and aircraft should not be on an approach already descending at that location.