For a definitive answer, you need to have an attorney review the employment agreement with you--in regards to contracts and agreements, the exact language is critical to determining your rights and obligations.As a general matter, if this agreement is an enforceable contract, the employer would potentially sue you for any losses which naturally and foreseeably flow out of your breach of it. For example: say that once you signed the agreement, they had to pay a recuiter a fee for you. Then if you take the second offer, that fee was paid for no good reason and they could sue you to recover it. So not only do you need to have a lawyer review the agreement with you to see what it requires, but you need to discuss the specifics of the situation, including especially anything the first employer has paid to or on account of you, with the attorney as well, to understand the extent of your potential liability.