JHE
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Much of the public grief may be genuine. Tyrants are loved as well as hated, and dictatorships don't function without the co-operation of the people. When Stalin died, hundreds were trampled to death in central Moscow as hundreds of thousands converged on Red Square to pay their respects in scenes of mass hysteria. Not all of it will have been faked. In fact most of it won't have been-Communist rule was never as popular as when Stalin was at the helm.
People usually grieve for their parents - even for nasty, cruel tyrannous parents. With the endless official propaganda in Stalin's Soviet Union and in the Kim dynasty's Korea, people were made to feel the tyrant was the beneficent father of the nation. It doesn't surprise me that there is genuine grief and distress.
However, I think there may also be relief and even glee among some, but of course these emotions will not be so openly expressed.