The Real Property Division manages city fee-owned and tax-foreclosed properties. They periodically have "sealed bids"which is where you make an offer in writing, in a sealed envelope. The highest sealed bid person wins the property. When the city has tax-foreclosed properties for sale, a list will be posted with the minimum bid amount. Buyers will be required to pay post-judgment taxes due to Tarrant County in addition to the amount of the bid. All properties are sold "as is" and are subject to redemption period if still within the redemption period.
Check out the link below to see what they have available. Good luck!
http://fortworthtexas.gov/propertymanagement/realproperty/