If the food is coming out undigested (indicating it has only been a very short time in
her digestive tract as opposed to
throwing up digested
food), she might have, or have had, a blockage of some kind. Could definitely be a hairball, but if she likes to play with cardboard, it could be a piece of cardboard. Hairball remedies are usually some kind of laxative like petroleum jelly mixed with malt for flavor, to stick to the hairball and glide it down.