You would be surprised how often this kind of nonsense occurs. Very mature right? I mean, if they expect you to adhere to the terms why would they resist sending them to you?
It could be that they no longer have a copy and in which case no basis for a claim later, but you may not want to rely on that. In most cases it is never worth it for an employer to sue an employee over a non-compete - but it certainly does depend and we have many employer clients that will take legal action even if it is an uphill battle.
I suggest you discuss your situation over with a lawyer in private so all the facts and circumstances can be understood. Most of us here, including myself, offer a free phone consult.
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There is no obligation for the employer to provide you a copy, however, I recommend you contact a lawyer to reach out to the company to request it. We do this on behalf of our clients. Generally it will be provided. We can assist if you'd like to contact my office.