Can I sue another driver's insurance

I live in Texas. My wife was in an accident with an unlicensed, uninsured, presumably illegal alien, but the owner of the vehicle he was driving has minimal liability insurance. The police report clearly states that the accident was his fault.

His insurance will not begin to cover all the medical bills, nor will it come close to replacing her vehicle which is a total loss.

I have underinsured coverage which will cover the rest of the medical bills, but I

OK, that didn't take all I typed.

As I said the driver appears to be illegal, and both he and the vehicle owner seem to be low income, so while I assume I could sue them and win I doubt if I could collect anything.

So my question is: Is there any way I can collect more from his insurance company than he is insured for? Or are they only liable up to the amount he is insured for? Do they assume any liability for him loaning his vehicle to an unlicensed driver who then ran a stop sign causing the accident?

You can sue the driver, owner and insurer and let them fight it out...and then try to collect the judgment from all three...normally the insurer will be capped unfortunately...but not always. You may want to speak briefly with insurance counsel as well.