Can a private employer find out about my expunged conviction?

Maybe. There are two ways that a private employer might find out about your expunged conviction:

    Even though background check companies are NOT allowed to report expunged convictions to employers, it is possible that a company might include this information in your background check anyway;
    If an employer does its own “in-house” background check on you, they may find the information in (public) court records about your case. Remember, expungement does NOT seal the court records from your case, so someone could still look up the original conviction in your files. However, it is still illegal for most private employers to consider an expunged conviction, even if they learn about it through public records.