Can's someone get fired for refusing to sign injury waiver?

[Jamie U]

A family member of mine was recently told that his company had stopped carrying workman's comp, and asked to sign a waiver saying that he wouldn't sue for damanges if he was injured on the job. He refused to sign it. Since this wasn't in place when he became an employee there, I'm hoping this will make it illegal for them to fire him for not signing.
We live in Texas, by the way, where workman's comp is elective.