I found this old airport in a nearby town:
The hanger doors still say "AIRPORT" on them; but there is no windsock or signs of other facilities. It is not listed on web or in MSFS; and there are now dirt access roads across the runway.
The lack of listing on the common sources ( FAA, TX State, county listings) would indicate that it is not a licensed public or private airport. Putting up a hangar with the word airport doesn't mean a lot and still would not be common knowledge unless it's, for example, marked on the field or on the roof of a building. So, no publication basically means pilots wouldn't know it existed.
I also found no record of a strip in that location in a search of abandoned airports
http://members.tripod.com/airfields_freeman/TX/Airfields_TX.htm
A bit of speculation... it's adjacent to Southwestern Adventist University. They are active in the missionary-pilot world and I found a reference to a pilot flying/repairing/rebuilding aircraft in the Keene area. It's possible that it
was a facility operated by the school (or 'friends') solely for use associated with their missionary roles. The significantly large communications tower and building on the eastern end would certainly ruin it for safe a/c operations.
Also interesting to note the small domed observatory near midfield...
But is it closed? How would a pilot know, other than the fact that it is not on charts? There is no "X" on the ends of the runway. I assume you could get in trouble landing there now?
-James
First question is: Was it ever "open"? If not a licensed airport then I doubt there is a legal reason for marking it after it becomes disused. Perhaps, if it was commonly known, it might be prudent - but then again, for how long. In farm country there are many 'strips' that are even more obvious than this one, but not published anywhere.
Could you get in trouble? Likely not if the landing was an emergency/precautionary one. Just for fun??? hmmm it IS Texas and the landowner likely has a 12 ga. with 00 loaded.. is that trouble?
Apparently the legal profession in the US wanted a simple (more arguable?) definition (FAR -Title 14 - Part 1.1)
Airport means an area of land or water that is used or intended to be used for the landing and takeoff of aircraft, and includes its buildings and facilities, if any.
---For further clarification, contact a lawyer

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the Canadian regs (in part) are as follows:
301.03 (1) Subject to subsection (2), where the operator of an aerodrome provides the Minister with information respecting the location, markings, lighting, use and operation of the aerodrome, the Minister shall register the aerodrome and publish the information in the Canada Flight Supplement or the Water Aerodrome Supplement, as applicable.
(2) The Minister may refuse to register an aerodrome where the operator of the aerodrome does not meet the requirements of sections 301.05 to 301.09 or where using the aerodrome is likely to be hazardous to aviation safety and, in such a case, shall not publish information with respect to that aerodrome.
(3) The operator of an aerodrome registered pursuant to subsection (1) shall notify the Minister immediately after any change is made to the location, marking, lighting, use or operation of the aerodrome that affects the information published by the Minister pursuant to subsection (1).
“airport” means an aerodrome in respect of which an airport certificate issued under...