My spouse gave up an entire severance package because of the ludicrous terms outlined in the agreement. She could have been sued for any comments she made about her employer in perpetuity if she took her severance, which was neither generous nor fair. Our lawyer advised us to walk away and didn't charge us for his time to look at it either.

I'm happy the two of you were able to do that, but many, many people would not be able to turn down the severance, regardless of how terrible the terms are.

Couldn't she be sued even after declining severance ?

No, signing the draconian contract was a condition of receiving the severance, so (as explained by our attorney) by not signing she was not bound by that contract. It didn't amount to much money wise, not even a whole paycheck, and we were fortunate enough to be able to pass it up.

the natural state of things is anyone can sue anyone. So unless she got them to sign a contract to not sue, they can sue her.

Sure. They could sue but they cannot sue for a slam dunk "breach of contract" suit. They would actually have to prove damages which makes any case much more expensive for the company.

Yes of course, but not with a previously agreed cause of action.

Why should a company give one then?

Because treating people fairly is one of the requirements for many (not all) to sleep peacefully at night. And because it's the right thing to do, and keeps your Glassdoor ratings up.