Several thousand people were gathered and quarantined on the island, where they died together. You can write that off as a crazy decision symptomatic of a time when people presumably still pooped in holes in the ground and thought the sun was a chariot, but not a few centuries later, when everyone did the exact same thing again.
When the Bubonic plague tore through Europe, the island was reinstated to its former "glory;" a final vacation spot for anyone with the plague. When the plague got worse, they lowered Poveglia's requirements from "plague sufferers" to "anybody with any sign of sickness at all." They also changed their policy of "let the infected die peacefully" to "throw them in a large pit (atop already-dead bodies), and set them on fire," which, was quite a leap. Estimates put the death toll at 160,000 on the island, where charred bones still wash up on shore.
As if this wasn't scary enough, in 1922, a mental hospital with a scary fucking bell tower was built on the island (an island, you have to believe still smelled like centuries of charred, plague-infected corpses).
That hospital was where everyone sent the allegedly insane members of society. Remember, these were before the days of the first (and still horrible) DSM I. Anyone could be thrown into an asylum, wherein anything could be done to them.
According to legend, this particular hospital featured a doctor who routinely experimented on his patients with such things as lobotomies (performed with a hammer and chisel), for what was most likely described as "shits" with a potential for "giggles." As the legend goes, the doctor tortured his patients in the bell tower (we totally saw that shit coming), and ignored their cries that they heard and saw the ghosts of plague victims.
The doctor was then thrown off the tower by the ghosts of plague victims and, while in the dirt struggling to stay alive, was "strangled by a mist that arose from the ground." We would actually be tempted to disbelieve that part if this were any other island. Though we guess a much more plausible explanation than "the doctor was murdered by plague ghosts" is "the doctor was murdered by all those lunatics he tortured."