Even if a person files an auto collision claim, they are not required to sue the at-fault driver. Sometimes, a person pursuing a claim against an insurance company chooses not to go forward with a lawsuit if the case cannot be settled.  In Texas, even after a lawsuit is filed, claimants have the right to take what is known as a non-suit. This is a notice that automatically ends a suit. However, if a defendant has filed a counterclaim against the claimant, the case would continue against the claimant.