Airport Manager reported an airborne conflict that resulted in a critical ground conflict when two aircraft landing on the runway at the same time.

Narrative

At approximately XA:03(L) the Airport Manager announced over CTAF of closing Runway XX-XY to conduct a Runway inspection; due to an aircraft experiencing loss of directional control. Cessna-172 (Aircraft X) asked the Airport Manager over the CTAF frequency if he could land on Runway XX before closing the Runway. The Airport Manager gave permission to the Cessna (Aircraft X) to land since he was on short final.Once the announcement was confirmed over CTAF; a Piper Cherokee (Aircraft Y); on downwind to Runway XX; announced his intention to land; made an immediate 180-degree turn; and landed in front of the Cessna-172 (Aircraft X). The Cherokee (Aircraft Y) successfully landed; continued taxiing to taxiway 1 on Runway XX. Approximately 500 feet behind the Cherokee; the Cessna-172 (Aircraft X) landed on Runway XX; both aircraft occupied the Runway at the same time.For future consideration; Airport management will not grant any permissions for pilots upon closing Runways for inspections following incidents of any nature: accidents; deviations; etc. Also; Airport management will file all incidents.