Is it safe for my cat to eat cardboard shavings?

My cat has had a cardboard Alpine cat scratcher. She's had it for years, and loves to scratch it. But recently she's been eating the cardboard shavings. She picks up the shavings with her paw, then chews and swallows them. She's doing this a lot now. I don't remember ever putting catnip on it because she doesn't respond to catnip. Are the cardboard shavings safe for her to eat? Could they hurt her?