And that includes them, the people doing the layoffs, who are employees as well. And what we often don't realize is that causing the pain to others most often causes pain to us as well. Human group output and productivity can rely a lot on trust, and if that trust is damaged, it can hinder all productivity.
The last time my company did layoffs they offered the same generous severance package afterwards to anyone else who wanted it. We had three people take the offer.
As far as actual people? Depends on their personal moral code and is why colleges make people take ethics, even if I don't think that results in anything other than more elaborate ways to justify doing whatever they feel like anyway. Most people would agree that you should minimize suffering in others if you can, but people who make it to upper management and C suites often got there by not being bothered by such scruples.
As far as the company is concerned, obviously there's no reason not to care aside from not wanting to lose any critical employees who value stability. That's why many of the labor protections we take for granted now were fought for many years in the past.