Suppose I cascade cipher A and cipher B to encrypt a message. Both ciphers use the same key. I know that theoretically, the security of the setup when used correctly is at least as secure as the most secure. In other works, if cipher A or cipher B is broken, there is still cipher B or cipher A protecting the data. Is it possible under any case for cipher A or B to "reveal" the key, since it's broken? If this happens, then the attacker would know both keys and be able to decrypt the text.
TL;DR: Can a broken cipher ever reveal the key directly?