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Unfortunately, employment in the State of CA is "at will" absent an agreement to the contrary. (Note, there is an exception to this rule for public service employees who have attained "permanent status," but that is something that takes years to acquire) At will employment can be terminated for any reason not amounting to discrimination on the basis of a legally protected trait (race, religion, gender, etc.) or retaliation for engaging in certain forms of legally protected conduct (filing a wage claim, taking FMLA leave, etc.). It doesn't matter whether the basis for termination is fair, reasonable or even true.
So, it would not be against the law to terminate an employee (or rescind an offer of employment, which is essentially the same thing) for failing to disclose they previously worked for the employer. It may not be a fair reason to take such action, but since employment is at will employers do not need to be fair in this respect.
The only way you would have a claim is if you could prove that this stated reason was merely a pretense to cover up the employer's true motivation of a legally protected trait or activity, as defined above. You indicate that your employer asked you "where you came from" and where you were born. National origin is a legally protected trait, so if you could argue that by asking you these questions your employer's true motivation in rescinding their offer was the fact that you are from a particular country or are a particular race, then you may have a claim for discrimination.
The problem as I see it is that questions about how you learned to speak Spanish and where you are from are relevant to assessing your Spanish speaking ability. It is not illegal for an employer to inquire about how an employee learned to speak Spanish, as the ability to speak Spanish is a job skill like any other. It's no different than asking an employee how they learned Microsoft excel. The other problem with alleging discrimination is that if your employer was truly motivated by your race or national origin, why did they offer you the position in the first place? If they realyl wanted to discriminate against you for these reasons, wouldn't they have just refused to hire you?
If you feel like you can overcome these questions and make a plausible allegation that your employer was motivated by race or national origin in rescinding their offer of employment, then your recourse would be to file a complaint with the Department of Fair Employment & Housing. The DFEH will investigate and attempt to mediate a resolution with your employer. That not forthcoming, they will either file a lawsuit on your behalf or issue you a "right to sue" letter, which will enable you to sue in civil court with the assistance of an attorney.
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.
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