So, just called the CBP Info centre, as well as the CBP at JFK airport
According to both sources, if his visa is a combination C1/D and B2 visa, then he can stay after his contract finishes without further ado.
If, however, the visas are separate, then once his contract finishes, if he wishes to remain in the US for a while as a visitor, he has to:
- Exit and re-enter the US in B2 status. The quickest and cheapest option, but may require a Canadian/Mexican visa depending on nationality
- Apply for a change from C1/D to B2 status (costs USD 370) by filing form I-539 and sending it to:
2501 S. State Highway 121 Business
Lewisville, TX 75067