If he had had a visa, but he didn't, read the post. And as he had been living here for years, if he did actually have a visa, it would have been multi entry so would not have required a re-entry permit. :-)
"What Now? his retirement visa expires in November 2024. ", nope, that extension is gone, done, dusted. Your friend needs to start the process all over again.
If however you are on an extension of stay and you get your ducks in a row, you could cancel your extension ahead of time, and then hopefully your new school would have all your paperwork ready to apply for a new extension (on the day your old extension expires) at your new office, (and of course work permit).
You are eligible for the 60 day visa exempt entry, which can be extended by 30 days at your local immigration. No problem spending a few days in Laos and then coming back on another 60 day visa exempt entry.
OK, guessing you are actually asking about a yearly extension, if so, then yes immigration does offer that option, BUT check with your local office what their rules are regarding income.
Guessing you are over 50, so apply for a single entry Non-O (retirement/over 50) before you come to Thailand, then that gives you time to get your ducks in a row for the yearly extension when you are here.