Just looked it up actually:
https://statutes.capitol.texas.gov/Docs/TX/htm/TX.33.htm#33....Basically they put a tax lien on the property, they just don't collect on it while the original homeowner is occupying the property.
I'm not a lawyer, but my basic understanding of this is that if it exceeds the value of the property, the estate can just let the city/county seize the house. Otherwise, they'd need to pay the deferred taxes in order to transfer the title to the heirs.
Obviously this is not legal advice.