Suppose Alice sends message $Enc(k_{AB}, m)$ to Bob where $k_{AB}$ is the common symmetric key. Next Alice sends a signature of $H(m)$ $\sigma_{sk_A}(H(m))$ signed under her private signing key $sk_A$ to Eve, where H is a secure hash function. Then, Bob decrypts the message and sends it to Eve where she verifies it with the signature. Here, either Alice or Bob can be malicious. If Bob is malicious, he gives the wrong message $m'$ to Eve, she can easily check this since the signature won't be valid. But if Alice is malicious and generates a garbage signature (or signature of some other message m''), is there a way for Eve to catch her?