Truth In Filing
All information you give must be true and complete to
the best of your knowledge. There are penalties for
withholding information or giving false information,
including penalties for perjury in regard to citizenship or
immigration status. If the information is incorrect, you
may not be able to receive benefits and/or you may be
charged with fraud.

https://www.twc.texas.gov/files/jobseekers/unemployment-benefits-handbook-twc.pdf