This was a particularly insidious one because the usual strategy of culling excess livestock doesn't work out when applied to dwarfs' pets (pets can't be designated for slaughter, and other means of making pets die will make their owners upset). With most animals, you can avoid the pet adoption issue by just not marking them as available for adoption, so you wouldn't have to worry about a dogsplosion, sheepsplosion, etc. Cats do not become pets through that system. Instead, a cat adopts a dwarf.