Beginning of the War
While Don Salvatore was in prison in the police station in Pike Creek, Shoreside Vale, the Yakuza were moving to Liberty City. They were stocking up on heavy weapons, including a Rhino. Toni was sent by Salvatore to steal the Rhino and destroy it. After that attack. the wife of the Yakuza oyabun, Toshiko Kasen, called Toni and asked him to destroy her husband and his organization. This was the beginning of many attacks that would severely weaken the Yakuza.
Her first request was to steal Yakuza weapons and bring them back to a weapons dealer waiting in Rockford, Staunton Island. Her second request was to attack one of the Yakuza's trucks with a large amount of money and burn the money. Kazuki became aware of his attacks as he saw Toshiko and Toni going to the opera in Fort Staunton together. Kazuki was gathering his men to kill Toni, but Toni got to Big Shot Casino in Torrington, Staunton Island and got into a sword fight. Toni managed to kill Kazuki and gave his sword back to a regretful Toshiko as she committed suicide by falling purposely backwards of her window.
By 2000, the setting of GTA Advance, Asuka got her revenge when she orders Mike to kidnap 15 supposedly Leone members (still uncertain but seems most likely.) and she would sell them back to Asia as slaves. By 2001, the setting of GTA III, she met former Leone ally Claude and asked him to cut his ties with him and order the death of the Leone Don Salvatore Leone. Claude killed Don Leone and then kills a number of Leone hitmen disguised as FBI agents sent to assault the Yakuza territory. Despite this, Salvatore's death doesn't seem to weaken or defeat the Leones as his position was possibly taken over by Caporegimes Toni Cipriani and Joey Leone. The Leones also stock up more powerful weaponry as evidenced by their shotguns used to attack the player once he/she reaches Saint Marks.