I know it's normal that cats like to tear cardboard into pieces, but why?
One of my cats has been doing this since she was a kitten (now 4 y.o). She never eats the pieces, she just rips any cardboard boxes into pieces all over the floor.
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Almost all the cats we have had (26 in the thirty years we have been married - yes, there are times when there are quite a few around here) loved to tear up cardboard. In fact, I attach pieces of cardboard to the their climbing furniture or just leave a piece flat on the floor.
Sure, you may have a mess to cleanup but can't you see how much they love it from how they behave?
Get some used corrugated cardboard boxes and cut them into flat pieces and give those to her. You may be able to get her to leave the boxes alone that way.