Depends. I've worked places that offered exactly these kinds of things - to anyone.

It can happen, but it's not common. Typically they offer the voluntary severance package to the departments or activities or programs they want to thin out.

Here, though, not only are you likely giving voluntary severance to the people who were going to leave during that time anyway, but you'll end up giving voluntary severance to people you have to immediately replace. For example, if the X-ray technician at the VA clinic takes the buyout, that medical facility isn't just going to stop doing X-rays. They'll have to hire someone to fill the spot. The overwhelming majority of the civilian employees in the federal government are in the VA, the defense agencies, and national security agencies - all of which have a lot of positions that just can't go unfilled without causing a major problem. A more thoughtful voluntary severance program would have extended the offer only to people who were in jobs that wouldn't need to be re-filled.

But thoughtful takes time. So you end up with this kind of haphazard kludge that isn't going to accomplish its goals. They didn't spend the time to figure out what jobs they wanted to cut vs. those they needed to keep. They didn't spend enough time fixing the details of the offer in a way that employees knew it would be enforceable. So they got a really low uptake with no assurance that they won't end up paying out more money than if they had done nothing.

Plus - why bother doing this? Typically a private company will do voluntary programs instead of just laying off because they want to preserve employee morale or avoid brand damage....but DOGE doesn't want either of those things. They want federal employees to be upset and fearful for their jobs due to the threat of involuntary layoffs. They want to convey the message that the federal government is not a wonderful and well-managed organization. They want the public to perceive that not all is right with the status quo at the government, rather than preserve positive brand identity.

It's just....careless. It's a thing that Musk has done before, so why not do it again - even though the circumstances are completely wrong for this type of program, and it appears that it's been utterly unsuccessful.