If you have $350 on board credit it means your on board account will show a credit balance of $350 the first day. Anything you charge onboard will then come off of that. - Spa, drinks, shops, excursions, photo's etc...
I don't know if they would give you a refund if you didn't spend it all, my guess is that they wouldn't because its called an "on board" credit.
But most of the time the credits are small enough that you can easily use them up. Just in the auto gratuities alone for two people on a 7 day cruise you are going to use $140 to $168 depending on which cruise line you are on...
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013