Permits aren't needed for stucco.

We live in South Carolina. We hired a person who removed the stucco on two sides of a 1120 sq.ft. home. I terminated the workers after one day when he could not produce a permit. What is a reasonable price for one days work? It took 3 people about 4 1/2 hours to do this work.

A permit isn't required for replacing stucco. I am sure a permit isn't required in Virginia, Maryland, Washington, DC, and North Carolina. The only place I know a permit is required for stucco is in some cunties in California an new construction, where the stucco is inspected. Replacing stucco is considered cosmetic, and a permit is only required for structural repairs and alterations
Not having a permit seems like an excuse to rob these people out of their hard earned money. If someone has a contract, whether legal or not, at least an agreement, the contract is to do the whole job. If you wanted someone to just demo the old stucco by the hour, you could have found a day laborer.
You may have found this person to be incompetent, and had a good reason to terminate them anyway. The not having a permit is an old excuse to rob people out of their hard earned money. Another old excuse to steal money is holding a bright light up to plaster or drywall to find nit picky spots when it is time to get paid, or usually payment is already past due.
I may be wrong, what it seems to me is that you are stealing. It may not be criminal, but considered a civil matter, but is just as dishonest as holding a gun up too somebody's head