Wow. In the USA, companies can basically fire anyone for any reason at any time (in my experience). And getting fired usually happens very quickly -- as in, that instant: "Please pick up your things and come with me. No, don't touch the computer, someone else will log you out."
But an employee that really wants to stay can be on payroll for quite some time. But he cannot work for another company during that time. He has to be available.
But most people, I think, take the severance pay and move on. I did.
Here, a "settlement" is something you might get if you were to sue someone for something and the court awarded you money.
Also, in the states, if you're laid off, you can apply for "unemployment benefits" from the state. If you're fired, you cannot.