There are many phrases that are used to politely (indirectly?) draw someone's attention to a potentially embarrassing aspect of their dress.
Some ask "Cat's died?" when they notice that the bottoms of your trouser legs don't seem hang down as far they are normally expected to be worn.
There are several possible explanations for the origin of this expression:
By saying 'Cat's died?' they are implying that you are deliberately wearing your trousers ...
1.... at 'half-mast', like a flag1 (because your cats have died!), whereas, in reality, they are actually calling indirect attention to the fact that your trousers seem unusually short and that you may wish to correct this 'dress malfunction' sometime!
2.... with their hems further up from the ground because ... your your cat used to catch all the mice, but now your cat is dead, the mice abound and could run up your trouser leg, given the chance.
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