It sounds like you're looking for a cipher where, if a man-in-the-middle adversary modifies a single bit in the ciphertext, that single change flips about half the bits in the decrypted message after the corresponding point.
Most early ciphers were specifically designed to prevent such small errors from propagating beyond the affected digit.
Some people define a stream cipher as a cipher where each digit of the decrypted message is recovered by combining the corresponding digit of the ciphertext with a pseudo-random digit generated independently of the plaintext or ciphertext messages. To those people, any cipher with the "avalanche affect" you are looking for is, by definition, not a steam cipher.
Other people consider ciphertext autokey to be a kind of stream ciphers ("self-synchronizing stream ciphers"), which were designed to prevent a different kind of small error ("losing synchronization") from propagating to the rest of the message. A single-bit error in a message flips about half the digits for some (generally small) N digits after the affected bit. Perhaps you could tweak such a cipher to make N larger than your entire message.
The Propagating Cipher Block Chaining (PCBC) mode was specifically "designed to cause small changes in the ciphertext to propagate indefinitely when decrypting" -- is that what you wanted?
Sometimes "decoding the rest of the message as gibberish" is desired to defend against Something Bad from happening. Usually that desire is better satified with a some form of message authentication or an all-or-nothing transform, as otus pointed out.