Usually the voluntary packages are set in stone, there are no compromises or individual dealings. When our company did it, we had about 4 weeks to decide to take it, but could opt out last minute for almost 2 months.
Management was given strict instructions that no deals to stay could be made. So those that stayed, took their chances. Many stayed, hoping the voids in higher positions would be filled by them, a good assumption considering 1700 people (out of over 20k) left, and in some departments 20-30%!
And for many of my friends, it did indeed work out that way. 10% raise with promotion, and higher bonus, if you still planned on 10 more years of w*rk, meant way more to them than taking the package and w*rking someplace else because they were not FIRE. Most of them did not have a pension (hired after they stopped offering them in 2008).
Some even with greater than 30 years and a pension, still stayed for reasons that were important to them (adult children with unusual disease/brain damage etc where the company HI would cover them vs having to take Medicare was a sadly too common one), some w*rk was their life, others in the middle of a divorce, but most commonly, the hope that a path to higher paying management would be possible without as much competition and so many slots opened.
Of course, the company counted on this, as they usually offered a package every 10 years or so, with each subsequent package less alluring. (I remember the first package had a month’s pay compensation plus a months pay for every year of service up to 24. Then it went down to 1+18. Then it was just 14 months pay max.).
They could easy trim aged fat without appearing discriminatory and honestly, most of the fat was older, tired, waiting for a package seniors. Younger go getters fill the positions for less than than the pensioners were getting paid, and that happened in a domino effect, where new hires could be brought in for less cost to the company than the positions vacated. Though this backfired for some in demand positions like engineering, where the shortage forced higher salaries since no pension could be offered.
Personally I had no problem knowing I was paid less than market because I was making more than I ever had planned, and a $55k pension (partially COLA) and low cost HI from 61-65 was worth a ton to me to be able to comfortably FIRE. The added cash bonus of the package easily compensated for almost 2 years of salary and increase to pension, which was my planned exit time.