We had an employee refuse to sign them after we fired them, for cause. A few weeks later he asked for a larger severence than we initially offered. We offered a month's worth of pay, and he wanted way more than that if I recall correctly. We said no. He then lied, said he was fired for racial discrimination. Threatened a lawsuit. We caved and gave him an extra month of severence. He signed the papers and took his two months of free pay.
Aside: I personally hired this person. I noticed big performance problems early, and personally mentored him for six months before coming to the conclusion that we needed to let him go. I was the one accused of racism. It hurt. I lobbied for more time to turn this hire around, I gave him so much attention and extra time to turn things around. Only to be lied about in the end. Worst moment in my career so far. I wanted to fight any lawsuit-- we had tons of documentation and evidence that the fire was 100% performance related including commits demonstrating clearly these problems (and extensive notes documenting the improvement plan). But our employement lawyer and the CEO figured it would just be easier to give the severence.
Anyway. You may have more leverage than you think. Though, just be ethical about how you handle it. They really need you to sign those papers just to tie up the legal loose ends.