The Forellis aren't mentioned that frequently besides Phil Collins's manager needing to pay off 3 million pounds to a Forelli member.
Tommy Vercetti was a Forelli member until he went to Vice City on orders of Sonny Forelli, the gang's leader. Tommy then loses $2 million and drugs. Sonny is furious and wants his money back. Meanwhile, besides getting Sonny's money, Tommy starts his own empire and loses connections to the Forelli gang. Sonny leaves Liberty City for Vice City and recieves $2 million in counterfeit money. Lance Vance betrays Tommy and tells Sonny that the money isn't real. Tommy then guns down both Sonny and Lance in his mansion.
Because of Sonny's death, the gang is severely weakened and is a minor annoyance to Claude, such trying to stop him from crushing a car with a dead body in it.