My understanding of the phrase ‘barn cat’ is that the cat lives in a barn, usually on a farm. Not all farm cats live in barns which is why I started with the meaning of ‘barn cat’.
Starting with that premise helps to formulate an answer to the question. A true barn cat should be semi-domestic, or looking at it from the other side of the coin: semi-feral. But the cat has to be tame enough to accept being taken to a veterinarian for regular treatment because he or she will need to have some human caretaking.
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This is because he’ll be hunting rodents or at least that is the intention. He’s almost bound to get fleas and worms. There’ll have to be regular checks and treatments for parasites. And of course the usual vet visit for other needs such as injuries.
Also he’ll have to accept human contact because the owner should feed him regularly and take care of him; be concerned about his welfare in the usual way. It would be wrong to demand that a barn cat entirely feeds himself. There may disagreement to that suggestion but that’s what I think. If there are farm animals in the barn the heating will be supplied!
So a good barn cat should have a wild side; be semi-feral but domesticated enough to accept and like human contact both with owner and vet and be an interested hunter. Not all cats want to bother to hunt. Some are better than others. It’s a individual trait.
It is probably accepted that it is very difficult to relocate feral cats from a colony site to a barn and farm life. It may not work.
I’d have thought that a suitable cat could be found at a rescue center. I’d like the views of others on that. A barn cat’s life is the modern day equivalent of the original domestic cats around 9,000 years ago. I believe that it is very good life for a cat. It is a very natural life. Although it would be a little harsher than the life of a true domestic cat. Therefore the lifespan may be shorter on average.
One last point; a barn cat would have to get along with other animals such as horses and cows. I have a feeling that cats are predisposed to getting along with farm animals. It probably comes naturally. In fact, I’d expect them to get along better with farm animals than people.