You're not supposed to eat those slips on paper inside a fortune cookie.
That's easy to do, as they taste just like the cookie.
After thinking for a moment about it, there are quite a few foods with paper in them, where you're not supposed to eat the paper.
Chicken: Giblets and neck inside are often wrapped in paper
Hamburger patties: Often separated by paper squares
Candy: Remember that candy... little colored sugar dots stuck to paper?
Roast meat: Paper frills are sometimes used on the ends of chicken drumsticks or rib bones.