Are There Any Penalties for Validators Who Fail to Sign a Block in a Proof-of-Activity System?

Yes, Proof-of-Activity systems can implement penalties for validators who fail to sign a block. These penalties, often referred to as "slashing," can involve the loss of a portion of the validator's staked coins.

Slashing is a mechanism to discourage validator inactivity or malicious behavior. By penalizing validators who do not participate in the consensus process, the network can ensure that there are always enough active validators to approve new blocks and maintain the security of the blockchain.

The specific penalties for validator inactivity vary from one PoA implementation to another.