Huh?
The others are sadly correct that there are no true "no kill" shelters. Your mom was probably this poor cat's last hope. They get abandoned, hungry, scared. The best way to save a kittie's life if you don't opt to adopt is to contact a private rescue where people take them into their homes. Unfortunately these rescues are often hard to find. It's possible your local shelter could have a list of rescues, but rescues are often at or beyond capacity but keep trying for as long as you can. As long as the cat can stay awhile, please don't give up. Sometimes local groups have Facebook pages. I'm currently trying to befriend a scared cat living outdoors who won't let me touch him. Canned food and treats such as "Temptations" will hopefully get him to eventually come around. I'm not giving up on him.
Keep doing that until he trusted you, I did that for years with stray cats, but don't turn him in to a shelter, they will kill him right away for being afraid!!ππΌππΌππΌππΌππΌππΌππΌ
From what I understand there aren't any no kill shelters ... you may want to look into someone who fosters cats, maybe they can help you ...
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