Assuming that the individual is an at-will employee (no employment contract), the employer can reduce the salary (or even terminate employment) so long as there is no unlawful discrimination (please see the page at the link below).
This information does not constitute legal advice and does not establish an attorney-client relationship.
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 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 terms of employment 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.
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Yes, as long as the reduction: (1) does not violate FLSA minimum wage or overtime law; and (2) does not violate any federal or state issues regarding discrimination. A full review of your hours and any events would be necessary to determine the propriety of the pay reduction.