My compromise is a large chain link dog enclosure, which is *roofed* over with more fencing. They have access to it via a cat door in one of the windows of the bedroom which is exclusively their room.
I live in the country, on a farm with lots of trees, shrubbery, and out buildings where cats can take shelter. To my knowledge, the coyotes have never ventured close because of the dogs, yet none of the cats who have wandered/been dumped here and which I have not taken indoors have survived for more than nine months, despite being fed and getting medical treatment as needed. They are being killed by predators of some sort. I find lots of dead cats along the road (people intentionally hit cats - it's a sport) and bury them, but none of them, so far, have been ones who lived here.
A note about feral cats - I disagree with the claim that they can never be happy indoors. My first experience with bringing in a true feral was Kate. It took a year to trap her, and by then she had a litter of kittens. When she finally went in the trap (this was on this farm), I took her down to St. Louis with me. It was my intention to get her healthy enough to be spayed (she was terribly run down from nursing), let her recuperate, and bring her back to the farm. By the time she was recovered enough to be spayed, she was following me around the house. Needless to say, she stayed. She was my best friend for eighteen years, and I will never again have that close of a relationship with anyone.
Of my current clowder, Y.A.C. is by far the most clingy, constantly underfoot, and fierce in his affection toward me. He too had never been touched by human hand until I trapped him to be neutered. Doc was aggressively feral - I almost lost use of my left hand from the bites I got from him while transferring him from a large trap my sister had to a carrier to take him to the vet, and he is now one of my most affectionate cats, even though it took well over o year before he let me touch him. Ayla, OTOH, may never allow me to touch her, although she is quite content to be in the same room with me. All my other former ferals are *normally* affectionate, and all are quite content indoors. About half of my sister's crew had never felt a human touch until she trapped them to spay/neuter. With the exception of one of hers, none of either her or my *wild* caught cats have the least interest in sneaking out. The only ones in my household that even think about getting through a door are Sebastian and Serenity, who were pets who were dumped.