We had a cat that occupied our garage for several years. He was a neighborhood stray that sneaked in one day when one of us left the door open, and while I tried to chase him out with a water pistol, that just made him cantankerous. He never let any of us get close enough to touch him, so we just put up with the snarls and hissing, provided dry food and water and a litter box and let him be.
He never wanted in the house and seldom ventured outside, and NEVER let any of us get close enough to touch him. I thought about trapping him for a trip to the vet for shots, but decided that it would be traumatic for both of us.
He lived about 5 years, and then one day the food and water were untouched and the litter box clean for several days. My search finally located him - deceased - in a cardboard box behind a workbench.
What kind of a life was that? It was what he chose and maintained, so I suppose it was the best we could do for him.
We have had cats for many years, and really enjoy observing the way they interact with each other and with us. the aphorism, “Dogs have families - Cats have staff.” is certainly more than just words.
Today we have two cats - Snowball, a white long-haired male, is 18 and far from the oldest we have had. And several years later Precious, a neighborhood female adopted and named by a family down the street and then abandoned when they moved away. Both would share the garage with the invader, but Snowball will not allow Precious to enter the hallway or bedroom areas of our house. He hangs out in the hallway, clearly to keep her out.
Perhaps you can offer to pay a neighbor for cat food....