1) There is no law saying that an ex-employer cannot discuss whether an employee applied for unemployment compensation or not. This is not the sort of "private" information that people have an enforceable privacy right in--after all, a number of people at both your employer and the UI office/department of labor, and any random person in the UI office if you go in in person, will know about your filing.2) As long as the ex-employer either only reports true facts or opinions, there is no defamation. So if the emloyer says, "John/Jane Doe is filing for unemployment," or "I think there's something wrong with someone who can't immediately get a new job," there is no actionable defamation--the former is a true factual statement, the latter is an opinion.However, if a false negative factual assertion is made about you, that could lead to a cause of action. So if the employer says, "John/Jane Doe has to file for unemployment because (s)he's an alcoholic and can't hold a job," that's (assming you're not an alcohalic) defamation.