TWC is kinda vague on this and require you to report severance so they can determine if you are eligible
Severance Pay
Severance pay is a sum of money that an employee is eligible to receive upon separation. Employers may have a company policy to pay severance pay.
You must report any severance pay to TWC when you apply for benefits or by calling a Tele-Center at 800-939-6631. Under Texas law, you cannot receive benefits while you are receiving certain types of severance pay. We will mail you a decision on whether your severance pay affects your unemployment benefits.
Wages Paid Instead of Notice of Layoff
Wages paid instead of notice of layoff are payments an employer makes to an employee who is involuntarily separated without receiving prior notice.
You must report any wages paid instead of notice of layoff to TWC when you apply for benefits or by calling a Tele-Center at 800-939-6631. Under Texas law, you cannot receive benefits while you are receiving wages paid instead of advance notice of layoff. We will mail you a decision on whether your wages paid instead of notice of layoff affect your unemployment benefits.
http://www.twc.state.tx.us/jobseekers/how-money-other-sources-can-affect-your-benefits