How do you know there isn't a very clear term in the employment agreement stating that upon termination you'll be asked to sign an NDA on these terms?
"I agree to follow unspecified terms in perpetuity, or return the pay I already earned" doesn't vibe with labor laws.
And if those NDA terms were already in the contract, there would be no need to sign them upon exit.
If the NDA terms were agreed in an employment contract they would no longer be valid upon termination of that contract.