No, it's a dummy cat – it's not stopped breathing.
Yet asking us has called into the air
the garden funeral there will not be,
homecomings from the vet there never were,
a life that's not, a Larkin's Coventry;
and where your kindness thus remains unspent,
the room's less warm around the non-event.
Above is a picture of the dummy cat in question. And indeed another dummy cat is in the background and yet another is off camera. All of them are presents from kin, the one in the picture bought, I gather, from the nostalgia chain Past Times. No one's ever mistaken any of our dummy cats for a recently-deceased cat, but quite a few people have mistaken them for real cats, and I find that oddly disturbing, in much the same way as misplaced solicitude.
The poem dates from 2003. Its publication was as an entry in an online competition, run by the magazine Your cat. It sank without trace when the competition page was taken down.