Bob, a non-pilot, is flying as a passenger with Alice, who is a pilot. Alice is PIC, but she is letting Bob fly the plane. (He's not certificated, but he knows enough to be able to fly under supervision.) If Bob does something in violation of the FARs, my understanding is that Alice is liable because she is PIC. Does Bob have any liability?
In most cases, Alice is the only one with liability. As PIC, she is directly responsible for the operation of the airplane.
Bob could have some liability depending on the circumstances. An obvious example is if Alice attempts to take the controls back and Bob refuses, he could be criminally liable for unlawful interference with an aircraft. Alice being PIC also does not protect Bob from being liable for any criminal acts he intentionally commits with the airplane.
That one almost certainly is going to fall onto Alice. Alice is pilot in command. She is directly responsible for, and the final authority on, the operation of that airplane, regardless of whoever was at the controls at the time.
But like anything else, there is always a situation that might fall outside of that realm. Chris suggested the idea of a passenger attempting to interfere with a PIC or required pilot flight crewmember. In these situations, Bob would bear responsibility under §91.11. Another scenario might be that Alice allows Bob to take control of the airplane, Bob commences the horse around with it against Alice’s objections, which causes an incident. I can see criminal or civil culpability landing on Bob’s shoulders for that. Now, if the incident happened as a result of Alice’s carelessness i.e. let’s say that Bob busted bravo airspace or a restricted area because Alice was ignorant or negligent of what was going on, it’s no different than of Alice was at the controls of the aircraft herself and did that.
It depends on what Bob does, and what a court or the FAA administrator determines. Liability is a legal term and is difficult to determine proactively.
One important basis for a determination would be that Alice is PIC so, according to 91.3 is "The pilot in command of an aircraft is directly responsible for, and is the final authority as to, the operation of that aircraft. " That goes a long way towards a determination of responsibility (which is not the same as liability).
However, there are things that Bob could do to violate the FARs. For example, if this is a part 121 operation, then FAR 121.580 prohibition on interference with crewmembers. could apply.