Legal Question in Legal Ethics in Missouri

Your posting is a little unclear. Certainly, an employer cannot enforce a prohibition of an employee talking to anyone while off duty. But, there seems to be nothing to stop an employer from telling an employee not to talk to a specific person. They just may not be able to formerly enforce that prohibition. Missouri is an At will employment state. Absent an employment contract, an employer can fire and and employee can quit without giving a reason, and with no requirement of two weeks notice.

If a former employee is now employed by a competitor of the employer, the employer might be justified in demoting or firing the present employee if the there might be a problem with trade secrets being divulged. That might require that the present employee be in management or have access to sensitive information. Sometimes, just knowing the combination to a lock or how much business the employer did the previous day, can be deemed sensitive enough.

An employer might fire a person if they violate the prohibition, but not state the reason, or give another reason. It would be up to the fired employee to prove that the firing was for a bad purpose. Talking to someone the employer doesn't like might be an okay purpose. But, if no reason is given, the employee would likely get unemployment, so the employer might be hesitant to fire an employee for just talking to someone.

Good luck