Is it possible that owning a business could be made into a 'will work for food' arrangement?

Sometimes small business will trade services "in kind" instead of for cash, but that's not anyone's normal mode of operation. Of course your problem is that even if you only accepted food as payment, the IRS still taxes that as income, and they only take cash.

You're free to sell your services for any sort of compensation you wish. You could take goldfish as payment. As long as your revenues and expenses pencil out.