Not sure there's a way for the employer to avoid both halves on the 941.    Seems like the employee would end up getting the amount paid in with the 8919 refunded to them at some point.....I've never had this situation before though.

I just ran across a free course that may be of interest https://www.cpaacademy.org/webinars/a0D4400000WmiFrEAJ

I don't believe the statues and Regs provide any authority for the employer not to remit employer's and employee's portions of FICA, even though the employee is primarily responsible for his/her share of FICA until is is collected by the employer and may have paid that over by filing a F.8919.

Since your question alludes to the filing of F.8919, my presumption is that it had already been filed with your client's return.  In that case, your client could file a F.1040-X to claim a refund based on the W-2 issued for the reclassification of his/her work status.

On the other hand, the employee's portion of the FICA which the employer had paid will be considered taxable income in the year paid unless it is recovered from your client.

Hope this helps.