No advance notice of termination or resignation is required.
If advance notice of resignation is given, it can be accepted, rejected, or modified by the employer.
If a notice period is rejected, the employer does not have to pay for the time not worked by the employee, since the duty to pay ends on the date the work separation becomes effective.
In general, an employer does not have to explain why it is letting an employee go - an employer can say as little or as much as it deems appropriate - an exception is in the situation of an employee who is discharged as the result of a background check covered under the Fair Credit Reporting Act (i.e., a background check performed by an outside, for-profit firm) - in that case, the employer must explain to the employee that the discharge is the result of the unfavorable report, give the employee a copy of the report, and furnish contact information for the firm that issued the report.
In most cases, it would not be a good idea to tell other employees why a coworker was let go. If curious people keep prying, the best response is to inform them that the company respects people's privacy and does not discuss personnel matters, and that they will need to ask the former employee directly if they feel they need more information.
Texas law does not require written notice of termination or layoff, but a simple, clear, and unambiguous written notice of work separation can help prevent employees from later claiming that they are owed additional pay beyond the work separation date, since they did not know they had been laid off or discharged, and they allegedly continued to "work from home", call on customers, or engage in e-mail correspondence with various parties as part of their supposed duties
Depending upon the circumstances, the following may need to be done at or near the time of work separation:
the employer needs to make a final wage payment within six calendar days for a layoff or discharge, or by the next regularly scheduled payday for a resignation;
if the employee had health insurance, the employer should give notice under state or federal COBRA laws;
in case of a mass layoff, the employer should give a WARN notice to affected employees and the state;
normally, except in the event of a mass layoff, no notice to the state of Texas is required for any kind of work separation, but if the employee was subject to a wage garnishment order for child support or alimony, the employer must notify the New Hire division of the Attorney General's office within seven days of the work separation; and
for employees who are under child support orders, the employer must notify the Attorney General's office (https://portal.cs.oag.state.tx.us/wps/portal/EmployerHome) within seven calendar days of the effective date of work separation, and in case of certain lump-sum payments of severance pay, bonuses, commissions, accrued leave, or similar post-termination payments, any child support or alimony amounts must be taken out of such payments.
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