Yes, the mafia built housing, but it’s not the kind of social housing we might hope for—it’s mostly slum-like. Of course, the city of Palermo is also EXTREMELY densely populated—I read something like the fourth-most densely populated city in Europe in a magazine once, but can’t source that now, so take it with a grain of salt.
Nota bene: I’m not Italian myself; my wife’s family has their roots in Sicily.
[1] https://www.marememoriaviva.it/ (website only (?) in Italian)