I've served as a fospice for Purrs Abound in MI. It wasn't intentional, but the cat they pulled ended up having issues beyond what we initially thought. I've never worked with/heard of an org that only takes in hospice cases, but I've had several from other orgs as needed. I have one old man now who has FIP so he'll stay with me until his QOL declines. He's from a shelter with municipal contracts, so they don't focus on any certain type/condition. They just happened to get him in as a stray.
Perhaps a rescue that focuses on medical/seniors? While many of those animals are able to be adopted out, I'm sure they get some that are near end of life and just need a place to live out their last days in comfort.
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Sam Maurice
Humane Society of Jefferson County
Jefferson WI
https://hsjc-wis.com------------------------------