My mother went through this exact exercise two years ago. Management was clear that, if not enough employees took the buyout, they would start layoffs with less generous terms. From previous rounds of layoffs she knew older employees were the first to go, so she took the buyout and got 52 weeks paid severance.
The day she resigned, she received a termination letter offering only 40 weeks. Fortunately the company stood by the more generous offer. But it took her the better part of a year to get a new job, and it pays much less than the one she invested 30+ years in. She’s from a generation when you worked at a single company for life, but companies don’t operate like that any more.
Off the top of my head, a couple of ways offers help in that respect:
Buyout offers soften the blow ahead of involuntary layoffs. They give people a sense of agency, which improves morale at a time when it's likely to be low.
Offers give people time to plan. Even if they don't take the offer, they'll have an idea of the numbers the company is looking to lose.
Offers help spread out the impact of layoffs. Laying off a large number of staff at once can cause organizational chaos; laying off a large number of staff over a span of weeks casts a pall over everything until the layoffs are over. Having people leave voluntarily gives time for an orderly transition without causing as much dread.
https://m.timesofindia.com/business/india-business/1000-veri...
I suppose that it is intended to increase worker motivation during reshuffling and reorganization when morale is likely to be low.
[0] https://www.cnbc.com/2018/05/21/why-amazon-pays-employees-50...