I think that if a agent or anyone that signs a negotiable instrument on behalf of a principal may be or become personally liable for the instrument. So, liability depends on whether the identity f the principal is disclosed and whether the parties intend for the agent to be bound by her or his signature. So if the agent signs on behalf of the principal they may be personally liable on the instrument. I think that liability depends on whether the identity f the principal is disclosed.
If the principal’s identity is undisclosed causing the agent to pay the third party. The agent is entitled to be indemnified by the principal and the principal had a duty to perform, even if their identity was undisclosed and failure to do so will make the principal ultimately liable, Adam would be the agent working for Beth who is the principle here, and Beth had the duty to pay Adam for her services, Adam could demand the payment from Beth.