Two Kilkenny cats decide the town is not big enough for both of them and fight until nothing is left but the tips of their tails. It is absurd rather than grim, and one of the odder jokes in the whole collection.
From Mother Goose / Nursery Rhymes (traditional). See the whole collection.
There were once two cats of Kilkenny.
Each thought there was one cat too many;
So they fought and they fit,
And they scratched and they bit,
Till, excepting their nails,
And the tips of their tails,
Instead of two cats, there weren't any.
Public domain. Text from The Real Mother Goose (Blanche Fisher Wright, 1916), via Project Gutenberg. View the source edition