According to an article in Atlas Obscura (link here), Italy has had some form of citizen registry since 1864, and then a census after World War II, whereby one's citizenship, and therefore one's access to government services was always tied to a street address. But some people traveled so often — circus performers and traveling salesmen, for example — they didn't have a permanent address in their home city. So a practice began of listing street addresses on streets that don't exist.
This practice continues today. In Rome, more than 19,000 people live on Via Modesta Valenti. But that street doesn't exist in Rome. Italy has about 237 fake streets with names, with names like Via del Comune or Via dell'Anagrafe.
Nowadays, Italy's peculiar system of fictitious streets is used less for trapeze artists or lion tamers and more for people who are homeless or precariously housed. Homeless people can ask to be registered as a resident of a fictitious street, which gives them an official address that they can put on their ID.
"Registering your address with the authorities is absolutely fundamental for accessing all the rights established by our constitution," says Romano Minardi, an advisor for the organization Anusca, which helps people with their civil registry status. "If you are not registered at a specific place, you don't have voting rights, the right to healthcare, social rights or even identity rights. If you don't have an address, from a legal point of view you don't exist. You're a ghost."