In 1945, Don Corleone was heavily wounded in an assassination attempt organised by Philip Tattaglia and Virgil Sollozzo. Gatto had called in sick that day, so he was not there to guard his boss. The family later found out that Gatto had been bribed by the Tattaglias. Peter Clemenza and Aldo Trapani were sent to kill Gatto. After this, they fled the scene along with Rocco Lampone to Paulie's Apartment. Here, Clemenza gave the apartment to Trapani to use as a safehouse.
One step up from squalid, despite the fancy neighborhood surrounding the place, Paulie Gatto's gift from the Corleone Family is this apartment, where he spends some of his time. This is, of course ,until he has no use for the place any more.