Unless you have a written contract of employment with your employer, you are considered an employee-at-will. This means that there is likely little protection afforded you relating to unreasonable supervisors/bosses, as well as the typical workplace politics and drama which can be so troublesome. In CA, employees are presumed to be "at will." At-will employees may be terminated for any reason—at any time, even a mistaken reason, they can have their hours or pay decreased and they can suffer a cut in their benefits, so long as it's not illegal or unlawfully discriminatory. Generally, employees who work under an employment contract can only be terminated for reasons specified in the contract. In your state, an employment relationship is at-will unless there is a defined duration for the employment contract or if the contract permits termination by the employer only under specified circumstances.
Unlawful discrimination would include an employer discriminating based upon a person’s Ethnicity, Color, Religion, National Origin, Gender or Disability.
So, yes, it is possible for the employer to let you go if you do not agree to sign the new agreement. However, with a name change for the company and a possible change in ownership, a new agreement is to be expected and unless it is significantly different from the original agreement you have, there may be little reason for concern.
Justification in quitting your job which might be persuasive to an Unemployment Insurance Appeals panel would include:
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