There's a provision in the severance paperwork that states that the non-compete they attached is one of the criteria for being able to receive the severance pay.
Yes, employers can and often do put these sort of provisions into such an agreement. If you have concerns about the non-compete, then you would be best served to meet with a qualified employment attorney as to same.
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White Collar Crime Lawyer
I agree with the advice provided by my colleagues. Including a non-compete as part of a severance agreement is common--and as with any contract you can always negotiate the terms of the non-compete. Understanding the restraints on time, geographic location and industry to which the non-compete applies is extremely important to know whether the amount of severance compensation you are receiving justifies stopping or limiting your capability to work in a particular trade, at least for a period of time. Know, however, that courts hold non-compete agreements enforceable so it is VERY important to consider the non-compete carefully. I also recommend consulting with an attorney to review the terms of the severance/non-compete agreement to fully advise you of your rights and liabilities.
This answer is for general informational purposes only and does not establish an attorney-client relationship.