A company does not have to provide you with a severance if it does a lay off or reduction in force. It simply does not have to, it is always a courtesy. Companies do it because the labor market is competitive, and lay offs will make it into some kind of publication if the company is old enough or large enough.
In Texas, employment is generally at-will, meaning an employee can be dismissed at any time and for any reason, as long as that reason isn't illegal under state or federal law.
The agreement must be backed by consideration. The employer must give something of value to the employee in exchange for the agreement. Employees must have 21 days to consider the severance offer, or 45 days if more than one employee is laid off as part of a group lay off.
Because Texas is an “employment at-will” state, an employer can fire an employee at any time for any lawful reason. Any lawful reason for termination may include a bad reason or no reason at all.