I had a similar situation back in 2009. I gave my resignation to my boss on a Friday and he said I should hold off until Monday. Monday came around and they laid off most the the dev staff. Instead of having to work for 2 more weeks I got 6 weeks severance and got to leave that day. I already had a job lined up to start 2 weeks later so I booked a week in Cancun in the interim. They make you sign a paper that says yo…
Making a counter offer can be taken as a refusal of their offer of severance.
Companies can't just not offer you severance if they make a habit of it so they may take advantage of being able to deny you the option.
I am not a lawyer but I know people who have lost their option of a severance simply by trying to negotiate for a better offer.