Layoffs and Reductions in Force Organizational Restructure and Employee's Rights

My question involves labor and employment law for the state of: Texas.

Hello, I work at a big company in Texas. We are going through organization restructure, and my role will be disappearing and I'll be put into a less favorable position. I'm assuming they'll be giving new "offer letters" for all the employees to sign for their new roles. What are some of the rights I might have in this situation? I do not like my new position as it blocks all the work I've done in career development. I think this might be a good opportunity for me to move to an industry I'm interested. What will happen if I don't sign the new offer? Will that be a voluntary leave or a layoff (thus getting compensation and allowing me to look for other jobs without too much stress)? Please let me know if you have any insights on this. This is the first time I'm going through organization restructure and I want to be able to act smart.

Thanks

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Layoffs and Reductions in Force Organizational Restructure and Employee's Rights