In general, no, there would be absolutely no basis to sue you for attempting to steal a client, as it is not illegal to compete. In fact, there is a strong public policy in favor of competition, and except in certain very limited circumstances, an agreement in which you were prohibited from contacting a client--even if SIGNED--would most likely be unenforceable.
As for being eligible for unemployment, you will be denied if the EDD finds that you were terminated for "misconduct," defined as conduct evidencing an intentional or reckless disregard for the interests of your employer. Attempting to steal a client from your employer could possibly rise to this level, since you should have known it was clearly contrary to their interests. It wasn't ILLEGAL for you to do, but the EDD will reason that you should have foreseen the potential that this would cause you to be terminated.
As for whether you should sign anything, that is really impossible to say without knowing what it is that you are asked to sign. However, you would have absolutely no obligation to sign anything, and you should have anything reviewed ny an attorney before signing. You should not sign anything impulsively or because you feel pressured to sign.
I hope that you find this information helpful. Please do not hesitate to let me know if you have any questions or concerns regarding the above and I will be more than happy to assist you further.
If you do not require any further assistance, please be so kind as to provide a positive rating of my service so that I may receive credit for assisting you. Very best wishes moving forward.
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