That is irrelevant unless the severance is contingent upon the non-compete agreement. As suranyi notes, it varies widely from state to state. In an employee-friendly state like California, non-compete agreements have to meet strict criteria (specificity, duration, et cetera) in order to be considered valid, e.g. if you come to work for TinySquash in the Stratrocumulous division you cannot leave and work for their direct competitor, Big Yellow Banana in any tropospheric development for X years; the intent being to prevent any employee carrying trade secrets from one company to another during critical stages of development. These agreements also have to have some consideration for the employee and so are generally part of an employment contract (typical for key development or executive positions where the compensation package includes large performance bonuses and other perks). In other, employer friendly states the non-compete agreement may have a wider applicability, but if it is so general that it would prevent the employee from seeking employment and create a hardship I can’t see a court enforcing it. I also can’t see an open-ended obligation to report on your future employment in perpetuity holding any legal authority. In a right-to-work state I supposed an employer could fire you for not signing it, legal or not, but I honestly don’t think an employer would risk the backlash of a lawsuit over such a firing.
I’ve been presented with non-competes three times in my career. One was with a manufacturer in response to some employees leaving and starting their own company; one was with a startup where I was offered a key development position; and one was with an aerospace contractor which also insisted that employees not discuss the agreement with each other. In the first case, I signed it in ignorance, and the company was bought out a year later by a competitor; as far as I know, it was never enforced on any employees as many went to work for other manufacturers. In the second case, I turned the position down (not specifically because of the agreement, but I had little confidence in the company being successful after talking with the principals, and I was correct in that judgment). In the third case, I consulted with my lawyer and flatly refused to sign it; I was pressured once by corporate management to sign, but after again refusing, the issue was dropped. I later left to work at a competitor and when the issue of non-compete was brought up, I pointed out that I’d never signed it, and it was quite entertaining to watch HR and corporate monkeys blaming each other for the oversight.
My rule now is that I don’t sign any employment agreements without reading through in fine detail and being assured that I’m getting some kind of consideration for signing it. If I don’t understand something, I take it to a lawyer who works in employment law. In my experience with these things, they’re rarely drafted or carefully reviewed by a lawyer and are generally written by ignorant corporate bobbleheads to instill fear, uncertainty, and doubt as some kind of bizarrely counterproductive management technique probably learned by reading Al Dunlap’s autobiography.