How does playing for "survivor" work in a Diplomacy tournament?
Not all tournaments are the same. But they all have some scoring system, which enables the various endstates of a game to be converted to a numerical score for the purposes of tournament standings. Here are some examples of scoring systems.
Most tournament games end in draws, either by agreement or time limit. Points are then scored by the players based on the supply centre distribution. In the event of a solo, under most systems the soloist gets a very large number of points and all other players score zero. Any exceptions to this rule are rare, and mostly occur in historical systems that are not in use any more.
Note that there are very few truly hopelessly lost positions in Diplomacy. The vast majority of those that are involve an elimination or a loss to a solo at the next Fall turn.
P.S. For Italy to go abandon the game and go into civil disorder in your example is rude to the other players. If this is happening in your games, you should find a place to play that has more reliable players (or at a minimum replaces players in civil disorder).