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It does sound like a nightmare job situation. I was not referring to an application, but an actual contract, so I shall presume you did not have one - certainly not one that dictated any restrictions on when your company can otherwise suspend you/fire you, etc. Because of that, in the eyes of the law you are in an "at will" employment relationship.
Generally, if there is no written employment agreement to the contrary, the employer has discretion to dictate the terms of employment; this would include promotions, job changes, lateral moves, salaries, etc. "At will" also includes the mutual right of employee and employer to terminate the relationship at any time, without notice, and for any reason. The only exception is that the employer is more limited in that "any reason" for termination or for differential treatment can not be due to reasons of illegal discrimination, such as discrimination based on race, religion, gender, age, disability, etc.
What this means for most of us, is that the employer can, unfortunately, yank us around quite a bit. It can change its minds, make mistakes, remedy them as it sees fit or not remedy them, etc. at its convenience, and the only real recourse we have is to end the relationship if we don't like it. It is a rather hollow right, I know, considering how much harder it is for employees to obtain other suitable employment, than it is for an employer to get a new suitable employee.
I wish the law were a bit more geared toward the employee, but it seems that employers lobby Congress and state legislatures while employees don't (for obvious reasons).
So, while I don't see any avenue there, there is a slightly different vein you might want to pursue: Someone accused you of stealing, someone made a false statement about you, to a 3rd party (employer) and it damaged you financial, in additon to your reputation. You may very well have a cause of action against that person for defamation - not only could you recoup your financial losses but it will teach the irresponsible speaker to confirmm his facts before shooting his mouth off. While these are not the simplest of cases, it is certainly worth looking into.
Let me know if you need some clarification and I wish you the best.
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