A Center Controller reported conflicting information with NOTAM; procedures; and personnel resulted in unknown runway safety status.

Narrative

Aircraft was IFR from the north landing ZZZ. When I read them the NOTAMS; I noticed that one of the NOTAMS was 'ZZZ RWY XX/XY WIP (Work in Progress) HVY EQPT'. There was no other NOTAM for a PPR (Prior Permission Required) required. I had the CIC (Controller in Charge) call the airport who told us to have the aircraft contact them on CTAF and they would get the equipment off the runway. This was accomplished; but I felt the situation was extremely unclear and moderately unsafe. The pilot seemed to agree; as when I initially read the NOTAM; the pilot asked 'so is the airport closed or not?'Suggestion: If there is heavy equipment on a runway; the runway either needs to be closed or there needs to be a clearly defined way to ensure the landing can be accomplished safely (PPR required). There was some debate between myself and others in the area as to whether I should instruct the aircraft to talk to the airport on CTAF; sort of a defacto PPR. I feel like this is relying on the pilot to ensure the runway is clear which is not their job.