Call me crazy, but based on the description in post #1, OP is at fault in this crash. Sounds unambiguously like a case of not leaving enough following distance. The first car getting cut off could be the cops fault, but the second following driver is 100% responsible for what their bumper hits.
From Johnson Garcia LLP in Houston
"So, who’s responsible for a rear-end collision?
If you are involved in a rear-end collision in Texas, you are not automatically at fault for the accident. In fact, you should ignore the erroneous belief held by most drivers that if you hit someone from behind in Texas, you will be automatically held responsible for the wreck. A judge or jury has the right to apportion responsibility between the drivers involved in the rear-end collision."
...
"Unavoidable accident
You must have heard that some accidents are unavoidable. These events happen but aren’t caused by the negligence of any driver. For instance, a wild animal might cross a busy road and end up causing a traffic crash. If a passenger in the vehicle is injured and files a lawsuit against the driver, the accused can claim that this traffic crash was unavoidable. "
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