A question about credit card fraud?

This is completely hypothetical but I was just wondering what would happen if someone gave their credit card number to someone and then they charged a bunch of things on it? Obviously the person would notice and report it but then what happens after that? Do they try track down the person or do they just refund the people? I own a home-based business and sometimes get people's numbers and of course I would never use them but what if someone did? It just seems like an untrustworthy system. What do you think?