After a few generations, their power was shattered by the Invasion of the Shalva tribe
The Kuru realm survived under Pariksit’s descendant, Janamejaya Pariksita, Janamejaya’s sons, his grandson Augrasainya, and probably beyond this. A closer reading of the texts yields more results for this still very hazy picture of Vedic history: the Kurus were overcome by the (probably non-Vedic) Salvas who “dispersed the Kurus from Kuruksetra” (JB 2.206, SSS 15.16.11 12,149) — a fact completely overlooked by the historians of old India.
- Page 21, Early Sanskritization: Origin and Development of the Kuru state.
The Puranas mention about furthur calamities like a flood that destroyed Hastinapura
His son will be Sahasranika whose son will be Asvamedhaja; his son will be Asima-Krsna, whose son will be Nemicakra. When Hastinapura will be washed away by the floods of the river (Ganga), he will settle down at Kausambi (Kosam, near Allahabad). He will have Citraratha as his son, of whom a son Kaviratha will be born.
- Chapter 22, 9th Skandha, Srimad Bhagavatam.
Chandogya Upanishad describes furthur destruction that befell the Kurus
At a time when the Kuru country had been devastated by hail (alternatively locust or thunderstorms), Usasti Cakrayana, with his young wife Atiki, lived in a deplorable condition in the village of the wealthy landowners.
- Chandogya Upanishad 1.10.1
The Bharata royal family was gone by the time of Brihadaranyaka Upanishad as sage Bhujya asks what happened to the Kurus and Yajnavalkya replied that they went to heaven
When we asked him about the limits of the world, we said to him, “Where were the descendants of Pariksit?” And I ask you, Yajnavalkya, where were the descendants of Pariksit? (Tell me) where were the descendants of Pariksit?’
Yajnavalkya said, ‘The Gandharva evidently told you that they went where the performers of the horse sacrifice go.’
- Section 3, chapter 3, Brihadaranyaka Upanishad of Shukla Yajurveda.
The Kuru kingdom existed in a weakened state even during the time of Buddha. However political power shifted first to Panchalas, then to Kosala and finally to Magadha. Whatever royal family remained there were probably uprooted by Mahapadma Nanda.
The Kurus still existed in Mauryan period, but as a minor republic (corporations or Sangha)
The corporations of the Licchivika, Vrjika, Mallaka, Madraka, Kukura, Kuru, Pancala, and others live by the title of "Raja".
- 11.1.5, Arthashastra.