In June 1938, the Board of Directors of the Texas Memorial Museum Centennial Coin Campaign, the group in charge of the coin's distribution and sales at the time, voted to end its multi-year commemorative coin program with the 1938 issues and called for all unsold coins to be returned after November 1, 1938 so that they could be returned to the US Mint and melted. (Of course, the recall only applied to coins still with official distributors of the coin and not coin dealers with existing inventory.) An advertisement to this effect was placed by the Coin Campaign in the American Numismatic Association's
The Numismatist magazine in August 1938; the Campaign's release was reported in multiple newspapers in July.
Texas Centennial Sales Halt Advertisement in the August 1938 Issue of The Numismatist magazine
The advertisement encouraged collectors to complete their coin sets while they still had the opportunity.
At the time, Charles J. Harris, the Board's Executive Secretary, commented that the stopping of the program well short of the authorized mintage of 1.5 million coins would benefit those collectors who purchased the coins due to possible market price increases as a result of their reduced availability. While this was a logical statement, it was a bit of a marketing ploy as it should be recalled that, by 1938, sales of the Texas Centennial coin had slowed dramatically (approximately 11,000 1938-dated coins were sold) and that 1.5 million coins would never have been needed/struck to meet collector/souvenir seeker demand.
Ultimately, over 156,000 of the 301,000 Texas Independence Centennial half dollars struck were returned to the Mint to be melted - ~52% of the coins minted. Not the highest percentage of the series, but a large percentage nonetheless. (For a quick look at higher total melt figures, see
Quick Bits #43 - To The Melting Pot.)
1934-38 Texas Independence Centennial Half Dollar

For other of my posts about commemorative coins and medals, including more on the history of the Texas half dollar, see:
Commems Collection.