Different types of contracts. An “at will” employment contract allows the employer to change working conditions (to the point of simply letting you go) but also allows the employee to walk at any time.
If both sides agree to some form of penalty for changing/breaking the contract, then it’s no longer truly “at will” and both sides are bound to contract or face the prescribed penalty.
I understand, if this was an at will agreement this girl doesn’t have much of a case.