Why do shot guns look like it could be sawed off to look like a pistol grip?

Yes I own a shot gun it was my first gun, There is 1 thing I love more then my shot gun and that’s my dogs (replacement for dog would of course be a girl I’m dating but I’m single so 🤷‍♂️) and love to keep her looking like Margot Robbie with pink and black eye liner (kinda like wolf of Wall Street ) But I’ve always wonder thing. Is there a history behind it or purpose or history and purpose which we no longer utilize today

Why do shot guns look like it could be sawed off to look like a pistol grip?
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