Underdog brands

Brands that start small as underdogs and evolve into a leader, how are they to handle the change in position?

Past couple elections around the world over the last year got me thinking about a challenge where a political party 'The brand', that played the role of an underdog one that was in minority, represented for the little guy suddenly wins elections and gets to the decision table grows in size and looses its identity as a small meek entity. Real life examples are the guerrilla organization, characterized as a terror group is now a legit party in power in Palestine. Barak Obama is running some of this same risk, promising nimble response to some of the economic problems is not running ever bigger size that slows things down, including lobbyists from every economic corner in the US into his government that he fought against.

What is a brand that has evolved from David into the Goliath to do? How is the brand to continue a successful relationship with its core consumers? Can the brand stay relevant to the cause? Do principles of creative destruction apply to such a scenario?