Second work permit question

Let’s say a person holds a job that supports them for an ARC and for unforeseen reasons that person’s hours slips below 14, so that person gets a second job with a work permit. Is the first job required to hand over the ARC to the second job? I was told (by somebody at Taichung immigration no less) you don’t need to do this as long as the total number of hours you have is over fourteen.