Requiring an updated W-4 does not subject an employer to an additional liability. Very importantly, the employer is already subject to additional liability by

Requiring an updated W-4 does not subject an employer to an additional liability. Very importantly, the employer is already subject to additional liability by the very fact of the employee working in another state/jurisdiction. It's irrelevant from the perspective of the employer's legal liabilities whether the employee goes through the formality of updating their W-4. But note that failure to update a W-4 after moving to another state or country is generally considered grounds for for-cause termination.