At the end of the 18-day Kurukshetra war in the Mahabharata, Duryodhana lost all his brothers and important warriors including Bhishma, Drona and Karna. Duryodhana died the death of a coward as he ran away from the battlefield. The story of the death of Duryodhana is found in the Sauptika Parva Chapter 9 of Mahabharat.
During the fag end of the Kurukshetra war, despair and fear gripped Duryodhana. He fled on foot and hid himself in a big lake called Dwaipayana.
The Pandavas soon found out the hiding place of Duryodhana and reached the spot.
The Pandavas taunted Duryodhana to come out and fight. Duryodhana replied that they can have the country for themselves, and he would retire to forest. Pandavas told Duryodhana that they did not want the kingdom as a gift from him but would fight and regain it from him.
Duryodhana agreed to come out and fight provided he was allowed to fight with a single person at a time.
Yudhisthira agreed and told him that he could fight with anyone of them of his choice.
Duryodhana’s choice was Bhima.
Both the warriors fought valiantly. Duryodhana had the boon that he would not be killed if he were hit on the upper part of the body.
Sri Krishna reminded Bhima of the boon. Bhima then hit Duryodhana on his thighs. Duryodhana fell down with his thighs broken.
Writhing in pain, he was left to die by the Pandavas. Soon his three generals Kripa, Kritivarman and Ashwathama reached there. They swore revenge. Duryodhana appointed Ashwathama as the supreme commander of the Kauravas.
The three went into the camp of Pandvas and butchered sleeping soldiers and the sons of Pandvas.
They then returned and informed Duryodhana of their dastardly act.
Hearing which Duyodhana was overjoyed and dropped down dead.