We rescued 2 barns cats and put them in the guest room to acclimate and they somehow got into the air-conditioning grate and are now wandering in my duct-work below my house.
We just stumbled upon that idea! We ensured there was only one vent they could come back out from, and we put some tuna fish in that bedroom. We have a small cam we set up and are vigilantly watching for them to emerge.
When they do, we have rigged a booby-trap with twine and we simply pull the twine from another room and it pulls some boxes on top of the vent.
We’re hoping this works. But hey, what else ya gonna do when snowed in?
On a more serious note, you may want to consder not just food but the litter box. Cats are pretty hygienic and if they can use a litter box they will. But, if they realise they can just nip out of the ductwork, eat/drink/do bodily functions, and then come back in, they’ll probably do that instead. Which means you’re screwed. Having racked my brains to try and get a kitten out of the tiny space between the back of the fridge and the wall without tearing down my kitchen, I feel your pain.
We played the waiting game and it paid off. We set up the booby trap and cam and waited and sure enough, mama cat came out with the kitten to eat/drink/etc and we pulled the twine, trapped them in the room, and now all is well!