Can an employee sue me directly for something the previous owner did to them?

Generally, this depends on whether you and the previous owner are, legally, the same employer for the purposes of the claim. In a share purchase, the corporation is unchanged, so a claim connected to something that happened under the previous owner's operation is still, legally, a claim against the same corporate employer you now own — an employee can pursue it against the corporation regardless of whose decisions led to it.

In an asset purchase, you're a separate legal entity from the seller, and conduct that happened entirely before closing, under the seller's operation, generally isn't something an employee can pin directly on you, since you weren't the employer at the time. The main exception worth knowing is where continuity of employment applies and the underlying issue connects to something ongoing that you're effectively continuing, rather than a clearly closed, past event.

This is a good reason to get full disclosure of any past employee complaints, disputes, or incidents during due diligence, and to make sure your purchase agreement's representations and indemnity reflect whichever structure you've chosen. A Treadstone business lawyer can help assess this exposure for your specific deal.