The abandoned apartment complex, as its name rather blatantly implies, is an apartment complex located in Little Haiti that is no longer in use by any tenants or administrators and thus could be deemed "abandoned". An Esperanto can be found parked outside. After Victor and Lance Vance discover that their associate Bryan Forbes is an undercover police officer for the VCPD, the two capture and imprison him in the complex to discover what he'd done with the shipment of cocaine Lance had left with him.
While the Vance brothers keep Forbes imprisoned, his missions are delivered from the apartment complex. In 1986, during Grand Theft Auto: Vice City, the abandoned apartment complex still stands but is inaccesible. However, since it still maintains its derelict appearance, it can be assumed that it continues to remain abandoned.