I had a friend who got RIF'd from a software company, and their offboarding paperwork included a 1 year noncompete that tied their severance as the consideration. Essentially, "we don't want you working here, but we also don't want you working anywhere else, either."
I got RIF'd and they included the paperwork signed at offer time for the non-compete. I didn't sign it thinking they would try to force the non-compete after the employment was terminated by them.
It's reasonable if the severance is equal to the pay you'd get over the term of the non-compete. They don't want you working for a competitor for a year? That's fine, if they pay you a year's salary.
However, in my friend's case, she was given the 1-year noncompete in exchange for 4 weeks' pay.
