Apolide means stateless: a person no country recognises as a citizen. Apolidia is the status itself. Italy has a formal procedure to recognise statelessness either through a court ruling or through a Ministry of the Interior decision.
Once recognised, a stateless person can get a special residence permit, travel document, and a path to faster citizenship after 5 years of legal residence in Italy.
"After years of having no recognised nationality, Sabriye applied through a lawyer in Asti and was eventually recognised as stateless. Her status unlocked a residence permit and a stateless person's travel document."
Statelessness is a recognised legal status. It's different from simply not having a passport or losing one. The procedure to be recognised is strict and requires solid evidence.
Official source
Ministero dell'Interno
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