With ebola today we hear about villagers "rescuing" infected family members from the medical institution, poorly enforced border control, estrangement of those who survived the disease, etc.
Were there instances of such things happening with the Black Death? I would guess it was a lot worse due to the lack of modern medical understanding.
One of the most sweeping changes were a result of the drastic decrease in populations. Most towns, villages, cities, more or less had to produce their own food in a local area, and the nobles often had large estates. These large estates required large amounts of workers; and the massive death toll meant that more laypersons were able to demand concessions, demand higher pay, more rights, etc., because they had a capital on manpower.
Essentially, large segments of the population (most of the population in some places), would have been wiped out, and the large plantation estate culture among the elite were forced to bow to the commons due to decrease in available workers.
There's a wonderful book called The Great Mortality, I believe, that basically chronicles the Black Death as it spread through Europe and came back around again in 1347/48. It is amazing how quickly it came and was over. It was an essentially alien disease, meaning most people were going to have no immunity of any sort. Plus everyone was around livestock all the time; buildings, mostly, weren't as solid and separate from the outside as they are today, and were also sources of warmth. This brings in parasites like fleas, but this hits pretty much everyone with equal fierceness.
There were no "plague centers" or any sort of quarantine areas. The lifestyle and construction of the time basically ensured that everyone was just as likely to pop a flea bite as anyone else. One day it was fine, the next half of your house was sick, half of the next door house was sick, everybody on the other side was dead, then a few days later there'd be fire pits in the city burning hundreds of bodies(happened in Italy), and within a month or so, its gotten everyone its going to get in a city, and its over with. Plague fleas come in with goods and produce, things that are being transported. They go to marketplaces, storehouses, streets carry them everywhere, trading fleas here and there across a city. Two or three days later, the wool merchant, his family, their servants, the merchants and transporters who supply them goods and services, all of their families, everyone those people associate with, and so on is sick. Two more days later and 30-40% of those people are dead, and another large segment of everyone you know is sick and bedridden.
The home was the hospital.
Most Christians thought that the world was coming to an end. For awhile people went crazy; massive redistribution of wealth (whole households are dead or abandoned), abundance of land, a new attitude of equality (the plague killed priests, lords, pigboys, etc. with no regard for goodness or station), etc. Whole towns of survivors got drunk, hoarded and looted, set fires, fucked in the streets, people formed big crowds, going town to town shirtless, whipping themselves, covered in dirt and blood, chanting, praising God.
Lots of Jew killings. Sightings of demons. Stuff like that.
Look into The Great Mortality by John Kelly. Easy to read, very well sourced, its very personal (based on letters, written accounts, etc).