Do I Need to Cancel My Extension of Stay When Leaving Thailand After Ending My Job?

If you are not looking to work in Thailand again then yes you can just exit the country no problem at all. However if you wish to work in Thailand again you will have go through a long process to re correct your exit upon application of your next work permit/visa

One last bit, I should probably qualify my answer a little more

If you never ever intend to work in thailand again, like if you're going back to your country and will only ever come back here as a tourist you COULD just go to the airport and stamp out and leave.

BUT

if you're ever gonna work here legally with the correct visa and a work permit failing to follow the cancellation process WILL mess you up down the road when you go to get a new Non-B extension at the immigration office for your next job. That's why I just tell people, cancel it the correct way, THEN you won't ever have a problem down the road if you're gonna work again.

So the answer is NO you cannot just stamp out and think things will be hunky-dory after that. Stamping out of the country does NOT officially cancel your extension.

Most people cancel their work permit then take that receipt and their termination paperwork to the immigration office a week or so BEFORE the date they're going to stop working. The immigration office will cancel the extension then give a new stamp that allows you to stay until the termination date on the paper.

THEN you can just stamp out of the country on that date.

Your extension of stay becomes invalid the same day as the reason of issue ceases. Hence, the day you finish work your stay finishes.

Your employer is correct

YOU GO to the immigration office with your termination paperwork and cancel your current extension of stay THEN you can leave the country