The result of the cipher should be indistinguishable from random, but can it happen that cipher produces the ciphertext that is equal to the plaintext as it also lies in the corresponding space? I guess it's just the probability is extremely low, probably equal to guessing the clear text on the first attempt, but just out of curiosity: is it theoretically possible and/or happened in real life?
The same goes to other types of cipher and e.g. hash function on small inputs.