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It only wins if it survives or finds what it needs, but there's no guarantee it will find it before it's killed or captured. It's quite possible that the Mafia or the Cult will kill it. But I'm thinking about removing the killing non-player characters from the Cult. Because a killing Cult isn't really a Cult...

Added 1 minute ago
And when the Cat wins, it simply leaves the game, but the other factions continue to play.