It's human's history for most tyrants and dictators to eventually fail...Ghandi said something along those lines.
Kira died?..."Kira who?" People returned to mind their own lives.
Though, I will have to say I guess crime spiked up a bit, maybe a bit too much, as if a rebound effect
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In the very last chapter of the manga, we learn a bit of the aftermath of the sruvivors, including Near...it even tells of a new but shortlasting Kira (PHAIL!!1!one!). In it, things are depicted as if the world simply returned to normal after Light's death
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