Your friend and co-worker may want to contact a lawyer familiar with Texas liability laws to find out for certain but in general if a person hits another person’s car, whether on a public roadway or on private property, they can usually be held responsible.
It is true that sometimes law enforcement officers will not respond to accidents on private property but that does not dismiss fault. Since the at-fault person did not have insurance for your co-worker to place a claim through she may want to make a claim with her own insurer, if she has collision coverage.
If she does not have collision coverage, or does not want to use her own insurance policy to make a claim, then she should see if she can take the at-fault party to court and get a judgment against him if he will not pay for the damages on his own.
Your coworker may also want to report the at-fault party to the Texas Department of Public Safety for driving without insurance. There are severe legal penalties for violating the state’s financial responsibility laws. A first conviction should result in a fine between $175 and $350 for the uninsured driver.