Generally, work assignments are the option of the employer. Absent any other compelling facts, such as the employer violating their own written policies, they can probably move you around.
What I hear you saying is that you don't agree to work at the new location. Is that correct? You can request a new assignment, but my guess is that the employer doesn't have to comply.
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An at-will employee makes a decision every time he or she goes to work to trade hours of precious life for money.
An at-will security employee, placed at a new post without explanation, who does not consent to work at that new post, can pound the pavement for other work.
Generally it is within employer's discretion to assign its employees to particular posts, unless the matter is regulated by a contract between an employee and an employer, or a collective bargaining agreement between management and the employees' union.
I do not believe a letter signed by an employee consenting to work at a particular post is likely to have created a contractual right of the employee to work at that particular post, in the context of at-will employment. A lawyer could analyze the specific letter signed by the employee to ascertain whether a contractual right was created by the consent. But if employment is held at will, it can be terminated for any reason at all, without explanation, by either party, and only unlawfully discriminatory or retaliatory reasons will make the termination unlawful.
Not legal advice as I don't practice law in Texas. It's just my two cents on the facts you describe in light of general principles of law. If you need legal advice, please consult a lawyer who holds Texas licensure. That's not me as I practice in Vermont ONLY.
Texas is an employment at will state. Typically, unless an employee has an employment contract, or is employed under a collective bargaining agreement through a union, the employer can modify or terminate the employment at any time with or without cause. If an employer, at any time, decides they no longer want to employ someone, for any non-discriminatory reason, that employee can legally be terminated. However, an employer generally cannot modify or terminate the employment for prohibited discriminatory reasons (such as racial discrimination), or in retaliation for certain protected actions (such as whistle-blowing). The situation you describe does not appear to constitute prohibited discrimination or retaliation.
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