Can a company enforce a contract requiring repayment of training fees?

A contract to repay training costs is enforceable. Generally, they are limited to recovering their actual, provable costs, possibly with some overhead or premium; for example, if in-store training, they could potentially recover the wages paid to the person who trained her (e.g. if she received 30 hrs of training by a $15/hour person, around $450--plus maybe some overhead, so possibly $500 - $600). That is the general case, because courts tend to not award outrageous or insupportable costs, even if specified in a contract, because such specified-in-advance (or "liquidated") "damages" are meant to be a reasonable approximation of the costs incurred, and are specified in advance just to simplify things. If they tried to collect an outrageous or excessive amount and your girlfriend contested it, most courts would award only what the other side can prove. The reason I keep writing "generally," "most," etc. is that you can't predict 100% in advance what a judge will do--you could get a less-learned or more dogmatic judge who does not actually analyze the situation but simply unthinkingly awards what the contract says. So yes, they can enforce the agreement; they probably can only get what they can show their costs to be be, more-or-less; but there is a risk they could get whatever is in the contract.