Advice I repeatedly hear is to “be sure to negotiate your severance”. But I imagine when you’re being told that you are getting let go, it’s probably too late to negotiate. Plus, your bargaining power has lessened since they no longer need you. I presume saying “thanks for the offer but I’m staying” is not a viable option either.
Do you say it to your boss and he/she takes back to HR? Do you work with HR directly and bypass the boss? Can they say “take it or leave it”?