Judging by the response to the Plague in the second half of the 1300’s, there would be efforts to gain retribution on whoever or whatever was the cause of the sudden depopulation. Conspiracy theories would abound, and people would lash out at targets that may or may not have caused the problem.
The world would be in shock, of course, and it would be difficult to reorganize society for a while. People wouldn’t really trust each other, and would fall back on their family groupings. Most people would be extremely defensive for a bit.
On the other hand, it could also be like what happens during severe weather, when people band together to help each other. Cooperation would increase, and people would take on a “we’re all in this together” attitude. The differences between nations might diminish.
The average wealth would dramatically increase, as living people took over the assets of the dead, such as remained. If it were a war that caused the decline in population, there might not be resources left. So a lot of what happens after the decline would depend on what caused the decline. A war leads to one set of consequences, and a comet strike to another. A plague of runaway nano-technology or a zombie invasion or the rise of a very virulent disease would cause still other reactions.
People would be crippled by lack of confidence and depression for a generation or three. People might lose the will to try, and suicides could also be a reason why the population was diminished so much.
The people who remained would probably be stronger than those who were killed off. I don’t know what their strengths would be—it would again depend on what killed the others. Those strengths would be what keeps them going, and they would be traits passed on to succeeding generations. Life would be both easier and harder.
I wouldn’t like to live through such a scenario. I don’t think I’d take a survivalist attitude and run off to an isolated piece of country and start living only on what I could do for myself. I would be one of those ones who banded together with others to cooperatively seek to assure our survival.