Yes, you can ask for such a letter once 120 days pass, but you can nevertheless continue working even if processing time passes the date mentioned on your WP EXT letter.Thanks, John! So it mentions "In cases where the 120 days have passed and no decision has been rendered, the applicant may request continued proof of authorization to work using the IRCC web form. "
I think it means we have to wait to hear back from IRCC for receiving another 120 days of working until a decision is made. So still not sure what should we do in the duration of submitting a webform and receiving a response.