Great question! Both stories illustrate how societal instability results from human shortcomings that ultimately cause societal collapse. Let me explain.
Lord of the Flies' (1954) plot relates the tale of a group of boys stranded on an island. They initially attempt to organize themselves by establishing a leader, assigning tasks, and creating rules. However, the boys' fear and violent instincts lead them to wage war against one another. They take pleasure in killing pigs, overpowering one another, and burning down entire regions of the island.
The Hunger Games (2008), similarly, portrays the dissolution of a political state built on violence and oppression. In The Hunger Games, Panem punishes the outlying districts for rebelling by requiring two individuals from each district to fight to the death. This event is then broadcast and celebrated in both the Capitol and the other districts.
Both stories suggest that humans crave violence—we enjoy it. They also suggest that the political systems we create are naturally imbued with this violence. This violence leads to instability, and the system collapses. Both stories illustrate how the defects in our humanity become the defects in our societies; these defects are what ultimately lead to societal collapse.
For more information, please explore the eNotes guides to both of these great stories, linked below!