It is common for an airfield to be closed - no fuel, no food, no maintenance, no office to pay landing fee
How does the lack of any of the above items close an airfield?
A large proportion of airfields over here don't have any of those things. If a landing fee is to be paid you put your money in the slot in the wall.
I once flew into an airfield in Norfolk. I'm pretty thorough (or so I thought) with the preflight, nothing was amiss and PPR not required. Off I went.
Landed and it was like I had landed on Mars. Not a soul about. Nothing in the NOTAMs, on their website or the Pooleys flight guide to suggest they were closed.
I think somebody else also made that mistake as I found a note attached to the clubhouse doors left by a pilot a few hours earlier asking where everybody was!
A pretty common occurrence where I fly.