You Do Not Need to - and Should Not - Sign the Severance Agreement Right Away
Emotions are raw when you are first handed a severance agreement, which is frequently delivered at the time the Employer is advising you that the Employer is terminating your employment. That is a bad time to make a major life decision (which decision can have big ramifications to you both monetarily as well as with regard to rights that you would be giving up)
Some Employers - generally the more unscrupulous ones - will try to get you to sign the severance agreement right when they deliver it to you. This is a red flag that something is amiss. You do not need to sign it right away. Almost all severance agreements contain a written provision that the employee has a certain specific period of time to sign and return the severance agreement (usually the employee will have 21 days or 45 days, but I also have seen 1 week to 10 days). That time is provided - sometimes by law - for the individual to duly consider and negotiate the terms of the severance agreement. This is an opportunity for you that should not be wasted.
You do not get bonus points for signing the severance agreement right away, and by signing it you are giving up valuable rights (and financial and other opportunities) that you may not have fully considered. You may also be in shock when the severance agreement is delivered to you (which frequently is presented in a meeting in which your employment is terminated), and that is never a good time to make a major financial decision.
Keep in mind also that once you sign the severance agreement you may very well be giving up/ “waiving” your right to negotiate for more and better severance, and you may also be contractually bound in other ways (confidentiality, non-disparagement, liable to the Employer for attorney fees for a breach, prevented from competing/ working at certain other employers). So think long and hard before you sign the initially proposed severance agreement - and do not sign it right away.