Haha not sure how it works in Japan but you’d never get me to agree to that in the US.
“Find another job ASAP or we might shut the branch down. Also if you quit, you’ll get a severance package and we’ll give you a glowing recommendation for your new job.”
It’s just how they word layoff and severance package. In Japan voluntary resignation can be also entitled for severance package depending roles/duration of employment, and this gives larger package than regular voluntary resignation is entitled to, to make them resign “voluntary”.
Also you can’t fire without cause here, and the burden of proof is on the employer should it be contested. Instead they do this and rely on the cooperation/feeling of obligation/“the implication” to get employees out.
Assuming they are all 正社員 (seishain) which are a class of full-time employee, the bar for dismissal is high. In fact, it’s common to basically pay employees to go away rather than to actually try to fire them or something. A company can, in actual financial hardship, lay people off. I don’t know what the bar for that is or if there are any criteria as to whom or in which order they must dismiss.