Demographic Crises
Social Effects
Agricultural societies have a couple of responses to demographic crises that are pretty standard, and they applied here. One is migration from the countryside to the city. Put simply, there were lots of jobs available in the towns and with the villages devastated there were plenty of reasons to leave the old homestead. Where it was legal, and even where it wasn't, the response of peasants was to flood into the cities. The result was that many of the towns recovered fairly quickly, and much more quickly than did the countryside. The obverse of that, of course, is that in certain areas the countryside suffered even more population loss.
A second response is a lowering in the average age at marriage. In general, people in a pre-industrial society married when they could support themselves, either with land or a trade. Both were in ample supply in the immediate aftermath of the Black Death and the result was the ability to marry at a younger age than before. This, in turn, led to a "baby boom" that tended to replenish the population.
Our sources to speak of shocking misbehavior during the crisis itself. Boccaccio is hardly alone in noting that the traditional social structures of family, neighborhood, parish, and commune nearly disintegrated while the plague was stalking the streets. This may not seem surprising, but it certainly surprised the people at the time. Nothing—neither war nor famine nor previous epidemics—had caused the fabric of society itself to fray. It was nearly as frightening as the disease itself, but society also quickly returned to normal. For better and for worse!
There's little evidence of social unrest, though. That would come later, but in the 1350s we see almost no social rumblings with the exception of the Jacquerie in France. That, however, happened almost ten years after the Black Death and was more as a result of the catastrophe at the Battle of Poitiers than of the aftermath of plague. I'll have more to say about this a little later, but the point I want to make here is that the catastrophe of the Black Death itself did not result in significant social change.