The technology to produce Damascus barrels developed for several reasons.

Originally barrels were being produced by wrapping metal around a mandrel and welding it longitudinally. These barrels were prone to burst along the weld inflicting great harm to the shooter. Damascus was seen as a safer method of construction. When damascus bursts, it is always in specific location. The very construction of the tube prevents a longitudinal burst.

As time and technology progressed, it became possible to economically produce round stock and bore it out to produce shotgun tubes. This lead to the demise of damascus.

In 1903, Liege produced 39,000 sets of sxs barrels. In 1906, they produced 159,000 sets. This huge increase in business lead some to start cutting corners and producing inferior barrels. One of the problems was that some makers stopped boring out the chemise. Fired splinters of metal would spew from the gun. This also set the stage for barrel obstructions. The better makers in Belgium were aware of this and spoke out against these shoddy practices.
http://damascus-barrels.com/files/Damascus-Barrels_dot_com_E_Heuse_Lemoine.pdf

I believe that many of the "problem" guns have since found their way to the scrap heap.

Pete

http://www.damascus-barrels.com/Movie.html