My employer often does the same thing and I really like my employer.

Telling her that she is unemployable by the company in the future is petty.

2 week notice is a courtesy, not the law. As an employer you need to take the high road. Employers being petty will always be a bigger deal than an employee that leaves without much notice. Particularly when it is done specifically to send a message to the other workers. It sends the message to others that you can give 2 week notice or zero day notice.

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