The employer may terminate the employee due to his or her criminal history, even if such was prevously disclosed, as long as the employee does not have a written employment contract limiting the reasons for termination--and, if so, this is not one of those reasons. That is because without a written employment contract, all employment is "employment at will" and an employee may be terminated at any time, for any reason whatsoever--or even for no reason at all (e.g. the employer just decides to terminatte them on a whim or because the employer is having a bad day).