PR process will continue irrespective of applicant changing or loosing the job.
If applicant need to work, they require a valid permit which implies work permit. To get work permit from IRCC, applicant need to submit OINP work permit support letter. To get that support letter, applicant need to submit the payslips, job offer letter (some kind of authentication that they're employed).
If applicant doesn't want to work, then they don't have to go through this hassle. Then they're deemed as illegal (or else they need to provide some sort of legal/ implied status).
Applicant can't apply for Bridging open work permit as your PNP work permit support letter mentions closed one. So, applicant need to apply for closed work permit from IRCC which has expiry as PNP work permit support letter (I assume).