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I live in DC and have a rodent problem. DC has a program that allows you to adopt a blue collar working cat. I think it is basically a trap-neuter-return type program, but instead of returning them, they give them to people who will give them an outdoor shelter and feed them daily. We are not looking for a pet and wouldn't want to commit to much more than a kitty tube (probably a DIY one), a small sand filed section of our garden for a litter box that we would clean regularly, putting out food and water in the morning, and maybe a heated cat pad for really cold winter days.

I understand that feral cats can be a touchy subject (bird lovers seem to hate them and cat lovers love them), but I am looking for an objective answer highlighting the pros and cons of essentially habituating a feral cat that my yard is a consistent place to get a meal and sleep. How much responsibility is having a working cat?

See the related post Can feral cats be moved? it has a lot of detail about moving feral cats. Reading your link blue collar working cat, they have a few words about the initial commitment, but not a lot. I suspect they will tell you more if you reach out to them.

In short the first couple to few weeks is going to require more work and responsibility for you. After that the amount of work goes down a lot. Feed daily and clean the litter box a couple times per week.

If you can handle the 'acclimation' commitment the rest is easy. It is a live animal that you are committing to support, so if you like to take long vacations, you will need to plan for someone to provide support in your absence.

Overall, talk to the shelter and be honest about your concerns and abilities to provide support. If they don't think it is going to work for you, they will let you know. Most shelters would rather keep an animal, than send it someplace that is not going to work.

James has a good answer, I used to work at a shelter here are a few additional things to consider. Most working cat programs require a covered shelter for the cats so they can stay dry in rain and have a place to stay warm in the winter. A majority of the programs also require you to take the cat to the vet on a yearly basis or if they are hurt or ill. Cats in working cat programs are not truly feral, they tolerate some human interaction, enough that they are not TNR'd they are placed with people who need mousers because they will get some care from humans but aren't expected to be as affectionate as a pet.

My boyfriend has 3 cats that's exactly how they live. They're not in any program and is not working cats they're just there. 1 came by 1 day had kittens and they all stayed outside in their yard.
Pretty much what you've said is really all they need.
There's shelters at the back, they get a bowl with fresh water and gets fed. Might get some extra things to nibble on here and there if they happen to see the cats and have something on hand.
He did catch them and take them to the vet if needed. He also got them spayde. So I think food shelter and vet care when nessesary. The cats goes to the bathroom wherever in the bush so you don't even have to worry about that. They're likely not going to use whatever litter tray you give them as they free roam they'll do whatever. Catch whatever they feel like in the wild.

Also since they know you they'll very likely let you pet or touch them but they don't have attachments or much emotions towards you. They're not totally wild I'll say they are somewhere between wild cat and a house cat. If l score them 0 is wild and 100 is complete house cat, they are around 60-70. So yeah he's had the mother for 14 years now and she's still healthy and strong like a young cat.