as an employer i can tell you this: the texas workforce commission is ruthless about benefits ON BOTH SIDES. when the time comes and you file for unemployment and your employer states you were fired for substandard performance, you can appeal and address your concerns with the TWC, they make the decision to pay, not the employer and they are fair, tough but fair, on both sides...this i know personally.
as far as the fraud you are claiming, i would tell you to relax. i don't know how young you are and what your long-term intentions are in the construction (i'm assuming) industry but most of the jobs are temporary. there is a lot of turn over and a lot of re-hiring that happens, it's part of the industry. so while you may feel your employer is trying to screw you, the fact is contracts end and people get laid off. whether or not you qualify for unemployment benefits has little to do with what your employer says about you and more with how long you've been employed there and how much you've earned there. sure your former-employer won't make it easy but they are not the ultimate decider.
if i knew my job were going to end, i would focus on trying to find another one (which you will have to be doing anyway in order to get unemployment benefits) rather than burn bridges from someone you may work for again in the future.