What happens to my Non-B visa when my work permit expires before its official date?

Work permit and non visa based on it?

IF you stay inside the FIRST 90 days you got on entry OR from the Immigration Office using the Non Immigrant B visa, you can sit out the 90 days and just leave the country.

IF

you visited the Immigration Office and applied for and got issued a 1 year Extension of Stay permitted up to xx/xx/xx (it is a big stamp in your passport, just have a look) you visit the Immigration Office again to inform that the conditions of this stamp did change,.

You cancel this Extension of Stay with the last day of employment.

In general it's your work permit and your work that govern the validity of the visa or extension. If you're on the original 90-day visa then you don't actually have to do anything but if you are on an extension then you must cancel the work permit and then go and cancel the extension and leave the country or find another legal way to stay within the country.

Totally depends if you have a VISA or an Extension of stay, let us know, then we can tell you the correct answer.