What will happen when there's a car accident, but the driver has no license. There is insurance on the car. The driver was cited. What will happen if there's no damage at all on either vehicle? It was a minor rear-ender. What will happen in Texas?

Did the police investigate? If so, they probably have already issued a citation to the unlicensed driver.

If there is no damage to the other vehicle and the other driver is unhurt then that is the end of it. But if there was damage or injury then he (or his insurance company) will come after the unlicensed driver and the car owner's insurance company for damages. In all likelihood the owner's insurance company will not cover this, because insurance policies cover drivers who borrow a car only if they are properly licensed. Since the driver was unlicensed, the driver and owner of the car will be on their own in case of a lawsuit.