[elzbardico]

Some cats have multiple houses. Lots of people love cats, and if a cat starts frequenting their houses, they will start feeding them and kind of adopting them. Cat lives in the new house for a few days, then go back to original house, stay for a while, and go to the second house, and so on.

[aivisol]

We considered this option, and since we live in a remote countryside, we actually asked the neighbors around in few km radius. None knew anything. Mystery still unsolved. Happened only once.

[NikkiA]

Probably stuck in a shed, barn or other outbuilding that is infrequently used by the owner. Cat goes in while door is open, sleeps, resident leaves and closes door, cat is now stuck. The cat however will hear an approaching human and rush the door when it's opened next.

It happens to cats all the time when you live near farms, you either get used to it or learn to keep your cat indoor.

(If you only ever 'adopt' stray cats, it's a reasonable coping strategy to consider their presence somewhat ephemeral)