Texas: Excess proceeds in a foreclosure vs a bank REO sale?

[Jim McGovern]

I know that in Texas if a property with only one lien against it is sold at a foreclosure auction for more than the amount of the loan being foreclosed upon, then the excess is paid back to the owner who was foreclosed on.

My questions relate to what happens if the property is not sold to a 3rd party at the foreclosure auction, but reverts back to the bank lender (i.e. becomes bank-owned REO property) and the bank later sells the property for more than it was owed at the time of the foreclosure.

Questions: Does the bank get to keep ALL of the proceeds from the sale of the REO property? Or does the bank only get to keep up to the outstanding amount of the loan that was foreclosed upon and the excess still goes back to the original borrower?

I'm just curious regarding the law, as it seems like IF the bank can legally keep the excess on REO sales, then there might be occasions when a bank has an incentive to discourage 3rd party foreclosure bidding on certain properties in the hopes that the properties revert back to the bank and can later be sold for much more.

Thank you.