Do I need to notify immigration when quitting my job before my visa expires?

Hi there, I would like to ask you something.

Situation: I am currently on a non B, yearly extensions since 2011 but will be leaving my current job at the end of September. The current extension is valid until 30th September. Plan is to fly out in the 30th, get a 60 day tourist visa, come back in and by then my old workplace would have cancelled my old work permit so then my new work will be able to start the process of applying for a new one followed by a Non B for the next job.

Question: Do I need to notify immigration that I will be quitting my current job, prior to flying out on the last day of visa validity, or it is okay to just let it expire? And if it is indeed required I would have to do it on the 29th, Friday and so would need to fly out on that day itself, right? I have been told that there is no need to notify/cancel it but since there is a plan to apply for another in future, I thought I would ask you guys here as it’s the best place to get proper info.

Thanks in advance and also thanks for providing us expats with the most accurate info on visas!