Yes, you can get sued in Texas for not paying your car. In fact, creditors can sue you in Texas for any unpaid debts, including car payments. Creditors have a certain period of time to file that lawsuit after you first become delinquent on your payments, and that time limit is called a "statute of limitations." If creditors file suit within that time limit, then they can pursue a legal judgment against you for the full amount owed, plus interest, late penalties, and court costs.
To enforce that legal judgment, creditors can use various procedures to collect, including wage garnishment, bank account levies, liens, and asset seizure. Therefore, it's important to address any car payment issues promptly to avoid the risk of legal consequences.