LMGTFY ...
I put in "Texas trailer registration law" into my search engine; here's what I saw:
The top return:
www.txdmv.gov
The DMV has clear instructions as to what applies, what to do, etc.
And this was the second return from the exact same search words ...
statutes.capitol.texas.gov
The State statutes tell you what must happen, and if you know how to read statutory code, you can also find the penalties for violations.
Often, if you do not register a vehicle as required, there can be penalties for late registrations, sometimes even including paying back registration for previous years (to some limit).
Every state is a bit different. It's always best to search and read the official DMV/BMV and state ".gov" statues if you want to separate the bovine manure from the real-deal.
Rather than ask a BITOGer what might happen to you, why not seek the right information from the official sources???