So there are two separate issues here. First is whether the employee has any legal basis to sue in the first place. The second is whether the particular viable causes of action that they allege are causes of action which permit the employee to name the manager as a defendant in the manager's personal capacity. Certain legal causes of action provide that only the COMPANY can be sued, whereas violations of certain other specific statutes permit the employee to sue their supervisor in the supervisor's capacity as an individual.
Fortunately, the analysis here probably doesn't need to progress that far because it's not illegal to terminate an employee for being a poor employee, even if the employee disagrees with that assessment. The general rule in all states but Montana is that employment is "at will" absent an express agreement to the contrary. At will employment can be terminated for any reason not amounting to discrimination on the basis of a legally protected trait (race, religion, gender, etc.) or retaliation for engaging in certain forms of legally protected conduct (filing a wage claim, taking FMLA leave, etc.). It doesn't matter whether the basis for termination is fair, reasonable or even true.
So, it would not seem based on what you have described that this employee could sue the company you work for, let alone you in your personal capacity. To sue you in your personal capacity, they would generally need to be alleging that they were terminated for complaining about wages owed to them or in retaliation for taking FMLA leave. Furthermore, they would need to prove that you exercised your own discretion in terminating them for these reasons. Those are the two primary cases where personal liability can attach and you can be named as an individual in a lawsuit for wrongful termination. Otherwise, though, the employee can only typically sue the company they worked for, not you yourself.
I hope that you find this information helpful. Please do not hesitate to let me know if you have any questions or concerns regarding the above and I will be more than happy to assist you further.
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