You go a few weeks before the last day mentioned in WP and passport to the Ministry of Labor to cancel your Work Permit and the Immigration Office to cancel your Extension of Stay on the last day of employment.
Your new boss in another province apply for a Work Permit at the local Ministry of Labor and you apply with his documents at the local Immigration Office for a NEW Extension of Stay.
The point is that the officer at the desk could not make the decision and handed the documents to higher or other officers but did not want you to wait until their decision is made.
You have to go on mentioned date, if you go early it could be that they will tell you the documents are not returned yet.
As I said all have to work together and as you are the owner of the work permit and you are the owner of the passport with your permission to stay, you have to act to get all done in time.
I guess you got a big stamp in your passport after a visit to Immigration with the text Extension of Stay permitted up to xx/xx/xx
This stamp has to be cancelled on your last day of working, you can apply for a new Extension of Stay, even one based on unable to travel but it is the Immigration Officer who decide to approve your application.
Cancel the currect Extension of Stay and work permit in advance and apply before the last day with documents from new employer for a new Extension of Stay and work permit.