I wanted to edit the Greater Shiryu part, because it has not either been destroyed or the Lesser Shiryu has absorbed it after Gai as Lesser Shiryu's Busoma stabbed Shin Matoba Greater Shiryu's Busoma through the stomach or chest. But because of plot-ex-machina Gai somehow got his humanity back as he did so, the Busoshin was not created or it was contained and was somehow given a different purpose. But as result either the Greater Shiryu was either destroyed (unlikely, due to all the previous talk about the Shiryu's needing to become 1) or it was absorbed into Gai and he now has both of the Shiryu's in his possession and seemingly has full control over them without any murderous tendancies.
During the Muromachi period, the Dragon Blacksmith was commissioned to forging a sword of fine quality for the Shogun. After succeeding in his task, he brought the sword to the Shogun, and to his surprise, was ordered to remove his mask. Reluctantly he did as commanded, and the court looked upon his face in disgust. Thinking that a demon forged his sword, the Shogun ordered the blacksmith's wife and child executed, and the smith sent to a deserted island after surviving many execution attempts.
Having lost everything there was only one thing left for him; death. But no matter how hard the smith tried, normal swords were no use; the dragon flesh he inherited prevented him from dying. And so with sorrow for his family, and fury and hatred for the Shogun that took them away from him, the Dragon Swordsmith forged the two Shiryu blades. The True Shiryu he sent to claim the life of the Shogun, and it succeed in its task by decapitating him at lightning speed. The Lesser Shiryu, was used to grant the smith the death he wished for. Because of the anguish and hate the smith felt as he made the two swords, the blades inherited his fury, and thus became known as cursed blades.