Legal Question in Employment Law in New York

Yes indeed an employer can terminate you for not signing a document.

Usually, this is done when the employer's policies change, or when the employer gets a new lawyer who points out the holes in their standard employment contract. Because New York is an employment-at-will jurisdiction (you can leave any time for any reason; they can fire you any time for any reason), your continued employment would be contingent on your acceptance of the new policy or the new employment contract as evidenced by your signature on the document.

THIS POST CONTAINS GENERAL INFORMATION AND IS INTENDED FOR ENTERTAINMENT PURPOSES ONLY. IT DOES NOT CONSTITUTE LEGAL ADVICE, NOR DOES IT CREATE ANY ATTORNEY-CLIENT RELATIONSHIP. FOR LEGAL ADVICE ON YOUR PARTICULAR MATTER, CONSULT YOUR ATTORNEY.