You'd try to domesticate a foreign judgment. Key word being try. But, again, you'd file it where they resided if you wanted to see a dime.

File "It" what is "it"? The lawsuit? Try to make at least a little sense, would you? This is a Texas law, so you file suit in Texas, receive a judgment in Texas, then domesticate and enforce the judgment in the state where the defendant resides.

With a foreign judgment you'd have to successfully defend it in up to three separate venues to even hope to domesticate it. Hint: none of them are going to be in Texas so best of luck

Not really relevant at all. What makes you think a state will refuse to enforce a valid foreign judgment, assuming all of the state's procedural requirements are met? It is possible that a court could refuse to enforce the judgment on public policy grounds. But this would seriously undermine the principle of full faith and credit.

Anyway, it's a $10,000 liability. It would cost more than that to defend against the suit and its enforcement. And even if you win, as a defendant, you're not recouping any fees.

And that's the real point. The people that will be bringing suits under this law will undoubtedly go to extremes to test its limits, and you're a fool if you think otherwise. Many of them support people who firebomb clinics and murder doctors. They are not really interested in getting money for themselves out of these suits; they are interested in using this law as a cudgel to bludgeon anyone who helps women obtain abortions.