You've asked a very expansive question, so you should consult a debt relief or bankruptcy lawyer, many of them including myself offer a free first consultation. But generally speaking, most property that most ordinary people own in Texas are exempt, or not able to be seized for unpaid judgments for such debts as hospital bills.
What is exempt in Texas? Your homestead, as well as $30,000 worth of "personal property" ($60,000 for a family), consisting of such things as household goods and furniture, clothes, a motor vehicle for each licensed driver, tools of the trade, two firearms, etc. Also exempt are life insurance policies and annuities.
What is not exempt? Examples of things that can be taken by judgment creditors are bank accounts (don't keep money in the bank if you have a judgment against you- it could be seized), tax refunds, stocks, bonds, boats, ownership interests in LLC's or corporations, and other luxury items or non-necessities.
The best way to handle this question is to meet with a bankruptcy attorney, have them review with you exactly what you own, then they can tell you if you have non-exempt property that you are likely to lose. If you decide to file a bankruptcy, and you qualify for Chapter 7, it may be possible to discharge or cancel the debt without losing any property.
Or, if you would lose property in Chapter 7 that you do not want to part with, it is possible to file Chapter 13, and pay your creditors what they would receive in Chapter 7, and thereby be allowed to keep the property.
It is a pretty darn complicated area of law, so I suggest that you consult with an expert in this area before you make any decisions. I am Board Certified in Consumer Bankruptcy Law by the Texas Board of Legal Specialization. My law firm is a debt relief agency; we help people file for bankruptcy.
While bankruptcy is an option, you should also consider your other alternatives such as trying to settle the debt with the hospital.
I have handled a few lawsuits such as these and have been able to settle the debt for very low amounts.