What if one is being laid off and the company offers them a severance package of X weeks pay for signing some papers?
That's not crazy -- they're compensating you for the inconvenience.
Whether that's a good idea or not is a different story, and would depend on how easily you could get a job, what it would pay you if/when you got it, and how much/how long the compensation would be.
In the oil industry it's not uncommon to see 1- or 2-year non-competes... with 100% compensation for the same amount of time.
Sorry if I wasn't clear, I meant signing stuff during your exit interview, so on your last day and quite literally on your way out the door.
Any reasonable company would do it this way unless they are trying to screw you.