Absolutely. And keep in mind that many managers seem to be bean counters that would rather fire people to lower costs than keep those people and be able to do actual stuff with them. Doing stuff takes imagination/brains and sometimes b*ls, and in my current experience that's not something to expect from management.
OTOH managers also like to retain people because headcount in one's org is a power/status thing, capacity headroom is good for absorbing unexpected work, and most important they don't actually benefit from cutting costs. At most, managers like it when other managers' employees exit