Your question is somewhat confusing in that you say your are refinancing YOUR home, but that you are not on the title nor on the loan.... In any case, judgments against you will show up in a title search on property that you own... that does not mean that they attach to the property.. If the property is homestead or the proceeds from the sale are going into a new homestead, the judgment does not have to be paid off at this point. That does not mean it is going to go away, it will continue to accrue interest until it is paid. You may need to hire an attorney to deal with the title company.
The Texas judgment lien is a powerful tool in the judgment collection process. Its power lies in its ability to attach your judgment debt to the debtor's real property. But, there are limitations to that power.
It Only Attaches to Some Real Estate
A Texas judgment lien only attaches to real estate your debtor owns. It has no effect on the debtor's personal property.
Now suppose your debtor does own a home in Texas. Your would, of course, assume that your lien attaches to that home. But, it doesn't. Texas exempts your debtor's personal residence from the power of a judgment lien. It's called a "homestead exemption."
Even though your lien doesn't attach to the debtor's homestead, it does create a cloud on the debtor's title to his home. In other words, you can make it difficult for the debtor to sell his home because your lien creates a question of ownership.
Because of this "cloud" you must release the lien as to the homestead. You don't have to do it until the debtor asks you to do so. But, if the debtor asks, you have to release it. If you don't, the debtor can sue you for damages.
It Attaches to Later Acquired Real Estate
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Disclaimer: This answer does not constitute legal advice. I am admitted in the States of New York, New Jersey and Massachusetts only and make no attempt to opine on matters of law that are not relevant to those three States. This advice is based on general principles of law that may or may not relate to your specific situation. Facts and laws change and these possible changes will affect the advice provided here. Consult an attorney in your locale before you act on any of this advice. You should not rely on this advice alone and nothing in these communications creates an attorney client relationship. The opinions expressed herein are those of the author only and the fact that he has worked as an Assistant District Attorney; State Supreme Court Clerk; Special Assistant United States Attorney (Hawaii); Assistant Cornell University Counsel or Judge Advocate, United States Marine Corps should not be relied upon to assume that these statements reflect the policy of these organizations.
There is actually a provision in the Texas Property Code that allows you to file an affidavit as release of judgment lien, under Section 52.0012. It provides for a 30 day prior notice of such filing to the judgment creditor and a suggested and fairly detailed form is included in the section. As a practical matter you may still have to do more to satisfy the title company prior to closing. But, at least, there is a mechanism to attempt to cure judgment liens that cloud the title to your homestead.