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This would not typically be advisable for a number of reasons. For one, it is not illegal to say nasty or "disparaging" things, it is only illegal to make objectively false statements of fact to third parties. In that case, a claim for defamation would arise.
The thing with a defamation claim is that truth is an absolute defense. This means that whatever you are contending was false this employee will have the opportunity to prove in open court is true. This can be an extremely invasive process, and the lawsuit will be public record.
The next issue would be damages. It's not enough that a defamatory statement was made. You need to prove specific damages--those damages will be what you stand to recover through a civil lawsuit. Unless you have extremely specific damages (i.e. you lost a contract because of what was said), it just isn't going to be worth the time and money to sue.
Finally is the issue of judgment collection. Even if you could obtain a judgment against this employee it would be a judgment against the employee in their personal capacity, which they most likely will not be able to pay. A judgment is worth nothing unless you can actually collect.
The far better option wouldbe to negotiate a non-disparagement agreement INTO the settlement agreement for this employee's wage claims. That is actually standard practice in any wage claim settlement and if you had an attorney I would be slightly surprised if they have not already proposed this.
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