What is the law in TEXAS regarding garnishment of a joint bank account when the other joint holder is not a spouse or significant other? Are there any protections for senior citizens receiving only social security income?

The account can be garnished ( if it meets the requirements of garnishment, laws on garnishment are very restricted in Texas as who is allowed to)

But the person who is not related to the debt will have their money frozen or even taken, they will have to prove to the court that it is their money, show deposits, give proof of withdraws and show exactly whose money is whose.

A joint bank account means that both parties equally own the contents. This means that a judgment holder can attach the whole account.

It is up to you to know prove what portion of the account was yours and what was the other party's.

Social Security income is protected, but once its in the account it becomes commingled funds and is subject to attachment. Again, you will have to prove that your share of the account was only from SS.