Yes, a correct encryption algorithm can encrypt (essentially) any bit string. But it's quite easy to turn a correct encryption algorithm into an incorrect one by bolting on something seemingly innocuous.
Here's a concrete example. Let's say you decide you want to make AES encryption more efficient by defining a new standard, "lzAES", that is just:
Enc_lz(key, msg) := AES-Encrypt(key, lzw_compress(msg))
Dec_lz(key, ctxt) := lzw_decompress(AES-Decrypt(key, ctxt))
This "works", in the sense that you can correctly decrypt ciphertexts, and it certainly seems innocuous. But it is now an insecure cipher!
Here's why: the definition of a secure cipher is that ciphertexts resulting from the encryptions of any two messages of equal length are indistinguishable. In other words, for any two messages you can choose, if I encrypt both messages under a randomly generated key, you can't tell which ciphertext corresponds to which message. In contrast, lzAES as defined above does not have this property: you could choose one message that's easily compressible (say, a string of zeros) and one that's not (say, a uniformly random string), and then you'd be able to tell which ciphertext corresponds to which plaintext just by looking at the ciphertext lengths.
And this is not just a definitional issue! If you use lzAES to encrypt something, an attacker can guess your message and test whether compressing the guess gives the same length as your ciphertext. Guess-and-check isn't possible with a secure cipher, but it is with lzAES---in other words, it gives away information about your plaintext!
Here's a concrete example. Let's say you decide you want to make AES encryption more efficient by defining a new standard, "lzAES", that is just:
This "works", in the sense that you can correctly decrypt ciphertexts, and it certainly seems innocuous. But it is now an insecure cipher!Here's why: the definition of a secure cipher is that ciphertexts resulting from the encryptions of any two messages of equal length are indistinguishable. In other words, for any two messages you can choose, if I encrypt both messages under a randomly generated key, you can't tell which ciphertext corresponds to which message. In contrast, lzAES as defined above does not have this property: you could choose one message that's easily compressible (say, a string of zeros) and one that's not (say, a uniformly random string), and then you'd be able to tell which ciphertext corresponds to which plaintext just by looking at the ciphertext lengths.
And this is not just a definitional issue! If you use lzAES to encrypt something, an attacker can guess your message and test whether compressing the guess gives the same length as your ciphertext. Guess-and-check isn't possible with a secure cipher, but it is with lzAES---in other words, it gives away information about your plaintext!