What many have described as voluntary layoffs I would probably call "voluntary resignation with incentives".
The company is asking you: Are you willing to quit your job and pretend we let you go?
It is wrapped around a layoff to be nice to the employee because this activates unemployment benefits, etc
What happens if nobody, not one person, volunteers? They layoff as many people as they need to, involuntarily, of course, as the term implies.
I had a case some thirty years ago when I worked at a shitty unionized company where I was asked (muscled by the union really) to choose between resigning or being laid off. The options had some convoluted combinations of benefits and legal implications (union stuff) that were hard for my younger self to decipher. I ended-up opting to resign, on paper. It was then executed as a layoff.