You Can Receive Unemployment Benefits Alongside Your Chevron Severance Package
What many employees receive from Chevron is considered a "conditional severance." In addition to payout, pension considerations, and more, the design of this severance package also yields a significant benefit that many professionals at Chevron often miss. To receive your severance, many companies require you to sign off and waive them from any hardship liability. By doing so, you then become eligible to apply for unemployment benefits. In wake of the recent Coronavirus pandemic, these benefits are substantially higher than in previous years and include higher weekly compensation, pay starting as early as the first week after employment, and an extension of unemployment benefits by 13 weeks.
Found this on google from a law firm. So you should understand what you are signing and what you need to tell texas unemployment office. HR should give better guidance.