In most situations, employment is at will and can be terminated at any time for any reason or no reason at all. The question here is not whether it violates that statute of frauds, but whether or not there was a contract of employment that would somehow take it out of employment at will.
This response does not create an attorney client relationship and is offered for informational purposes only. Only a lawyer fully versed on the facts and circumstances of your case can properly advise you on the case. I am licensed to practice in Minnesota, not every state. You should always consult with an attorney licensed in your area on how best to proceed.