1) An employer cannot refuse to accept resignation: your employer can't make you keep working after you decide to quit. It is therefore irrelevant if they "refused" the resignation initially--if your wife resigned, she resigned. So she quit in this case.2) They cannot make her repay a cost of a class or test, etc. unless there was an agreement made *before* the cost was incurred that she would reimburse them. Without a prior agreement, they cannot take the money from her check; if they do, she could file a complaint with the department of labor, who may help; or if the department does not (or is moving too slowly), she could sue, such as in small claims court, for the money.