Without dwelling on the ethics/morality/etc. of training contracts, if you really want to know whether you'll need to honor it, take the contract to a lawyer and pay for a consultation. Some good points have been introduced on how you may or may not be held responsible.

We run into lots of unenforceable contracts in our daily lives (ever read the back of a theme park admission ticket? Even in the case of the park's gross negligence you can't sue them?) A contract may or may not be worth the paper its written on.

NOTE: LostInPA is not a lawyer, never will be a lawyer, nor does he/she/it play one on TV