Before 1350, there were about three different models for hospitals. In Byzantine regions, the chief model was the municipal hospital operated in Constantinople. It was funded by tax money, and it actually had some surgery and active medical care in addition to charitable poverty-old age care. Italian cities ran municipal hospitals on the Byzantine model, often connected with their university medical schools. If you wanted good care when you were sick, your best bet was to get sick in Milan or Bologna.
Crusaders brought home this new idea, so the Byzantine model improved French, English and German hospitals. These hospitals tended to run on another model, the private-donor religious hospice. Often located in manor or town houses donated by the dying, they mainly cared for elderly poor people and orphans. Medical care was usually limited to heat, food, and rest, three things the poor did not have. Most hospitals took in orphans left by the dying or on a doorstep, and used the orphans as orderlies while giving them basic schooling. Private hospitals tended to have a charter that restricted them to certain issues, such as blind people, lepers, pregnant women, or the elderly. But they often took care of a number of different kinds of people, and their first priority was to make sure their patients attended Mass to pray for the souls of donors.
The third model was based on the infirmary of the Roman camp, and was chiefly followed in monasteries. One of the early monastic mandates had been to establish these infirmaries and make them available to travelers, as well as to monk residents. Monasteries used a lot of herbal medicine, in addition to food and rest. Crusaders also used this model when they copied the Byzantine one; the Order of St. John was originally a monastic order for taking care of sick pilgrims in Jerusalem.
The Black Death heavily disrupted the hospital system. First, they were simply swamped with sick people and had to decide how to manage the infectious epidemic. Second, they became swamped with orphans. A city hospital with a typical load of 20 orphans found itself with 200 and unable to feed them. Third, of course, their own nursing staff died as fast as anyone else, leaving them unable to maintain care.
Many small hospitals continued to exist in name, but they closed or combined with others. Some used their limited staff and funds to keep up the top priority: saying Mass for the souls of past donors. They had been not only care institutions but, as in modern times, also fundraising machines. Their donations patterns were thrown into chaos as businesses and families collapsed, but some continued to get money through land assets. Waste and fraud abounded.
The post-plague period saw a huge loss of faith in public institutions, including hospitals. Hospitals were audited and many closed; new foundations were started on more transparent principles. Private hospitals that could no longer afford to stay open deeded their houses to towns, who then had to determine how to fund them. Care for orphans, the elderly and disabled, and infectious disease victims were more rigorously separated. Donors began to found alms-houses specifically as retirement communities for the poor, with the obligation of perpetual prayer. Nobody could yet call the hospital system outside of Italy “organized,” but the Black Death nudged it in that direction.