The ending of 2 Fast 2 Furious resolves the Verone case cleanly: Brian and Roman take Carter Verone down, and their records are wiped clean as promised. Spoilers follow.
The takedown is built from three beats in the final job. First, Brian and Roman escape the police. Second, Roman disables one of Verone's men, so the arrest does not rest on Brian alone. Third, Brian crashes a car onto Verone's yacht, and the two subdue him. That last beat pays off the film's street racing setup: the driving that got Brian arrested in Miami is what ends the case.
The final job also works as a way out of a trap. Verone had already learned he was being watched, fed Monica Fuentes false information and planned to kill Brian and Roman, so the escape from the police and the yacht crash are the pair breaking out of his plan rather than carrying it out.
Afterward the deal is honored. The records are cleared, and Brian and Roman keep some of the money they recovered and use it, in part, to start a garage in Miami. That garage is the only lasting change the film leaves behind.
Production context explains the scale of that finish. Screen Daily reports a budget more than double the first film's $40 million, and the finished 2 Fast 2 Furious spent $76 million on a story that closes on a car yard in Miami, not on a larger threat. John Singleton directed, Neal H. Moritz produced and David Arnold scored it, according to the same credits.
Against the rest of the series, the ending is self contained. It sets up the two friends as a lasting team but does not tease a further storyline, so nothing here is a cliffhanger. In release order the next film is The Fast and the Furious: Tokyo Drift, which sits sixth in chronological order. To follow Brian's story in chronological order, continue to Fast & Furious, the third film on that timeline.