Mario Falcone is the son of Carmine "The Roman" Falcone, Gotham City's untouchable crime boss. Mario was hardly in anyway associated in the "family" business, Mario always seemed interested in more legitimate business. Mario was first introduced in Batman: The Long Halloween, but later made a more important, longer role in the sequel Batman: Dark Victory. But during the Long Halloween series, Mario was deported back to Italy through an INS loophole. When Mario did return from Italy he was interested in cleaning up the Falcone name, so he tried setting up business enterprises with Bruce Wayne. Naturally, Bruce declined his offer because Mario is a Falcone for which both Bruce and Batman are judgmental towards.
Mario was very adamant about legitimizing the Falcone family name by buying all of the stock in Falcone Imports established by Carmine "The Roman" Falcone. After buying majority sharehold in the company Mario evicts his own sister Sofia Gigante Falcone, trying his best to rid Gotham City of the organized crime element. Through out more of the story Mario helps the police and DA Janice Porter even more by occasionally helping out the police with information on the illegitimate business's administered by the Falcone crime family. For which Mario expected to receive protection.
But in essence Mario did all he could by eliminating the bad Falcone name and starting a new one. The only time through out the story Mario helped his family was by excepting Alberto Falcone or Holiday in to stay after Alberto was paroled after the Arkham breakout. But at the end of the story it is noted that the end of the Falcone crime family ended not with a broken women in a wheelchair but a broken man, Mario.
After all Mario's sister died after founding out that she was the Hang Man, his brother Alberto was a Holiday killer also, who died not from a bullet but from the hands of his own sister. He had been going through paranoia and failure the whole story which would seem to drive him to insanity. His father is dead also and body missing, no wonder why he doesn't want to be associated with the Falcone family.