An employer could make the statement, "He didn't show up for a scheduled shift, so I fired him." For UI, the failure to show up can be classified as voluntarily quitting even if the employee says that the employee was fired for not showing up to work. It is thus possible that the employee has been consistently telling people that you quit.

Further, to support a defamation case the present claim would have to be untrue, and would have to result in damages. It's not clear that an employer's statement on the one hand that you "quit without notice" and on the other that you were "fired for not showing up for work" would be seen as materially different by any prospective employer that contacts your former employer for a reference.