The prince in question was Yuyutsu. He was a step-brother of the Kauravas - Dhritarashtra was his father, but Gandhari wasn't his mother. He was opposed to the ill-treatment of Draupadi, and switched sides on day 1 of the war. He was however a mediocre warrior and easily defeated by warriors like Ulooka (son of Shakuni)He survived the war (which is why it's strange that Dhritarashtra felt that he had no sons left). After the war, the Pandavas asked him do do the funeral services for the Kaurava dead, while they did it for the Pandava dead. After Yudhisthir's rajyabhishek, he was made a minister in the Pandava government. And when the Pandavas handed over the kingdom to Parikshit, they made him the prime minister, and left Parikshit in his & Uttara's care.One thing that struck me was that Vikarna, who was one of Gandhari's sons, had been more outspoken about Draupadi's treatment, and yet didn't follow Yuyutsu's example. He too could and should have crossed over, so that Gandhari couldn't have complained that she had lost all her sons. Instead, he fought and died @ Bhima's hands on day 14 - the day Jayadrath was killed. Also, he was not the last Kaurava to die before Dushashan - in fact, even after Dushashan's death, there were still some Kauravas left alive, and they were all killed on day 18 by Bhima. The last one he killed before Duryodhan was someone names Sudarshan.
Thanks for the clarification😊
I always had a confusion with Yuyutsu and Vikarna. I remember Vikarna because he was the one who opposed insulting Draupadi. I had once read somewhere that Yuyutsu's mother was a maid of Gandhari, who used to take care of Dritarashtra during Gandhari's pregnancy. This has resulted in the birth of Yuyutsu. I think he was insulted by the Kaurava princes because he doesn't belong to the royal family. Vidhur was also the son of a maid. But he was very wise and judicious. Similarly here Yuyutsu was also a son of the maid; but was more sensible and judicious than the princes born of royal blood.