Our shelter is a non profit with a city contract in which animal control operates out of our facility and we are required to take in any stray animal that comes our way. Similar to how you have to balance the resources capacity you have with your foster network, we also have to take into consideration our capacity and resources when people want to surrender. We've been able to take the time to develop a waitlist for potential surrendered animals so that we can try to manage intake and schedule in surrenders when we can. Along with this we also provide a list of local rescues who do not have to deal with the mess that is our stray intake, rehoming resources (which can also be found on our website), we have some programs for vet care if that is the reason for surrendering, and we have a behavior help hotline where they can contact our behavior team (which includes cats!) for advice on what they can do in the home to help with behaviors. I've even given away supplies when I can if that's what they need, like trying out different types of litter and litterboxes for litter box issues in the home. And at the end of the day, if you've tried everything you can think of to keep the animal out of the shelter and the owner has tried everything they can think of to fix the issues or rehome on their own, sometimes you just have to take it in for the benefit of everyone.
For your purposes I would suggest a little smaller scale of what our shelter does. Maybe create a waitlist where people can email or submit in person applications for surrendering and when they do that immediately provide some local resources for rehoming or nearby rescues. From there you can review their case and get back with them with either advice or scheduling a time that they can bring in the cat. This would give you more time to prepare and search your foster network for people willing and available if you do end up taking it in, and can make the transition a lot easier since it wouldn't all be last minute. Doing this would also ease the mind of the owner a little, knowing that they aren't immediately being turned away. I'm not sure if this varies but animal abandonment is illegal where I am so if they threaten or you're worried about that, you can always remind them of that fact.
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Laurel Wilton
Feline Welfare Supervisor
Nebraska Humane Society
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