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I'm a little skeptical - if it was a "big" dog, they're not exactly easy to nibble to death. Plus a dog could outrun a squirrel any day, has larger teeth, and is a natural predator. More likely something else killed the dog, and the squirrels were after the body.
Of course, I've never seen a squirrel in real life, and if true, I'd say the town people should make sure their gun barrels are cleaned.