Not all Kauravs were exterminated, one Kaurav survived in Mahabharat

Gandhari was pregnant with the hundred Kauravas for two years. Dhritarashtr was worried that Gandhari would never give birth. As the precaution, Dhritrashtr had a child from Sughad, a woman from Vaishya Varna, also was a daasi of Gandhari. Sughad gave birth to Yuyutsu, he was born at the same time as Duryodhan and Bhim and was elder to Dushasan, other Kaurav and Dussala. Thus, Dhritarashtr had 102 children.Yuyutsu was the only Kaurav who survived the Mahabharat war beacause he fought for the Pandavas. All other 100 Kauravs were killed by Bhim. Yuyutsu wanted to be on the side of the ‘Dharm’ and he felt that his brother Duryodhan’s evil mind would also lead him to ‘Adharm’ so he chose the righteous side, which was Pandhavs. So at the beginning of the battle, when Yudhishthir proclaimed that anyone who wanted to, could join the Pandav’s side, Yuyutsu decided to join.

Yuyutsu is celebrated as a moral warrior who chose the path of righteousness, despite being born in circumstances that predisposed him to evil. He forwent his family bonds in order to side with the Dharma. It is to be acknowledged, Yuyutsu saved the life of Bhim by informing the Pandavs about Duryodhan’s cunning schemes, which included poisoning water. Both Yuyutsu and Vikarnabhorred Duryodhan’s conspiracies and evil schemes. However, Vikarn stayed loyal to the family and perishes in the war.ImageSource

Yuyutsu survived the war. Later, he was made the king of Indraprasth. Afterwards, Pandavs gave the throne of Hastinapur to Arjun’s grandson Parikshit as Pandavs decided to retire from the world at the start of the Kali Yuga (Kaliyug) and the departure of Krishna. Yudhishthir gave the charge of supervising the kingdom to Yuyutsu and he served as one of Parikshit’s two regents, since Parikshit was too young.

Dusshala (Kaurav’s sister) also survived. But technically she didn’t take part in the war.