Anytime the foreclosure auction yields less than the balance, either on the first or second (or even third) lien, the borrower is responsible, but Federal law, not Texas law, provides some protection. An attorney can explain what the law allows.
If you have sold a property as a "short sale" instead of allowing it to be foreclosed, the lender will frequently offer to forego pursuing deficiency as part of their approval of the sale. But they don't always do that.
If the lender has not tried to offer a loan modification or other HAMP/HAFA deal, and you have not tried to sell as a short sale, then at this point with foreclosure looming, not many options are open to you. However, you should consult legal counsel to find out if there is any other option available to you that makes sense.