If, by "legal trouble," you are asking if this is a criminal act, the answer is "no." However, this may be a violation of company policy.
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 (including a reduction in compensation which doesn’t violate the current minimum wage laws, or a change in location) 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. Additionally, when an employee violates company policy or engages in certain types of improper behavior, the employee can be terminated "for cause."
Note however: an employer generally cannot terminate an employee for prohibited discriminatory reasons (such as racial discrimination), or in retaliation for certain protected actions (such as whistle-blowing). What you describe does not sound like prohibited discrimination or retaliation.
I strongly suggest your company consult with an experienced labor and employment attorney for specific advice on how to respond when employees violate company policy.
Your question has been answered as a courtesy. This is not paid legal advice. Nothing in this communication is intended to create an attorney-client relationship. Unless expressly stated otherwise, nothing contained in this message should be construed as a digital or electronic signature, nor is it intended to reflect an intention to make an agreement by electronic means.
If she just picked up mail out of its usual place and opened it then no, there's probably not anything legally that would happen to her.
However, that does not mean that she cannot or should not be disciplined appropriately by you/the employer. I would also point out that if you have a chronic problem with employees opening confidential files and confidential mail that you may want to revisit your policies on how your subordinates have access to those documents.
Employment Employee wages and minimum wage Privacy law Discrimination in the workplace Racial discrimination in the workplace Employment forms Employment contracts Employee rights Employee privacy rights Protections against employer retaliation Whistleblowing in the workplace Employee break laws and work hours Paid time off and work hours Types of employment At-will employment Racial discrimination Discrimination Personal information