Yes! Dry cat food could go bad like people food if left opened. So the crunchy kibbles will be harder to chew especially for older and younger felines.
It can absorb different smells like smoking, cooking, etc. and its taste will be gone.
So it would help if you stored it properly like in tightly sealed container to maintain its freshness and original taste.
There should be no whole in your food packet, so make sure after receiving your package.
Toss it away after its expiry date to save your feline health.