The question though is if they are under implied student status on the study permit extension application if, in the meantime, they have completed their studies. In my mind, this would make the application for an extension moot if they are not beginning a new course soon and no longer intend to study in Canada.
As for the PGWP, you can still apply for it without student status (i.e. after 90 but before 180 days post-graduation), but you can't benefit from implied status as a worker in that case, and must wait for the permit to be approved before beginning employment.
Still, it certainly is an unusual situation and I could be wrong. It might be best for OP to raise a webform about it and get their status sorted out sooner rather than later.