The old axiom applies here too - everything is negotiable. I’ve personally negotiated many, both for others and even for myself. It’s surprising, but it’s true.
You may have some special circumstances (like someone in the company willing to fight for you) that inspires them to want to be flexible.
Also, there are other things besides salary to negotiate, for example, keeping your cell phone, your computer or even your company car. You can negotiate these things as an outright gift or to be borrowed for a period of time. Outplacement (career services for people laid off) is also negotiable.
Consult a labor lawyer to get specific advice about your circumstance and how the laws in your state apply to you so you know your rights.
You typically should’t sign anything at the moment you’re notified.
It’s very unlikely that they’ll withdraw the offer. Companies are offering severance as a way of maintaining good will with their remaining employees.
They may not be willing to negotiate, but I’ve never seen a company withdraw a severance offer because someone tried to negotiate.
The important thing is, like with any other contract, consult an expert before you commit to anything. In this circumstance, because the HR department represents the company, they’re not the best source of advice. In a good company, they’ll tell you that.
