 Cats also like boxes because they're curious in nature. When we bring a new box into our home, they want to know what it is and what's in it. Well, since your cat likes to play in boxes, just be careful you don't seal up your cat in a return package box and ship it back to Amazon like a Utah couple did who were perplexed when one day their shy cat, Galena, suddenly disappeared. For six days, Galena spent time in a box without focusing.