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cat out in the drizzle isn't good
Perhaps a box could be provided?
More concerned about the lack of chip tho
There are legions of cat owners who fit this profile. Have a look at cat groups on Nextdoor. It's a constant battle by the cat charities to get so-called pet cats chipped and neutered and jabbed against disease. My last cat rescued herself from a neglectful owner by asking me for help. She was paranoid about not being fed, smelly because no tray and scared of other cats, never been to the vet, owner didn't know what gender she was. Later on I caught one of her brothers who'd been feral for years. A charity rehomed him.
Maybe cat isn't getting enough attention at home. Who knows.
But cat out in the drizzle isn't good.
If the kids and wife like the cat, you have a cat in the day and no need for the expense of feeding nor vet. Sounds like a win.
More concerned about the lack of chip tho.