Is this a trick question? With ATM cards and plastic accepted almost everywhere, few people have any cash any more. Unless you've driven on the turnpike or other toll road and you owe the toll, then if you give the toll taker attitude about the situation, then, yes you will be arrested. I saw a smart guy in a Porsche blow a toll once and get a $500 ticket. The state troopers were having a great laugh over the situation and couldn't stop themselves from sharing. The other time you may get arrested is if you have eaten at a restaurant and you have no cash or workable plastic. Those are the only times in my limited imagination I can think of being arrested for not having any money. I'm sure there are others.
This answer is provided for informational purposes only. Actual legal advice can only be provided in an office consultation by an attorney licensed in your jurisdiction, with experience in the area of law in which your concern lies.