We model the political stasis trap as a dynamic network game in which cohesive elite networks transform political crises into system-preserving events. This provides micro foundations for the persistence of extractive equilibria across political transitions that existing theories cannot explain. The framework operates across three interlocking layers: a domestic network game, a sovereignty bargaining game, and a cascade model of decentralized predation. The model is calibrated to Madagascar (1960--2025), where five major crises reset the game's players but not its rules, generating a 17.8 percentage-point extraction gap between the social optimum and the predatory equilibrium. The 2023--2025 crisis provides out-of-sample validation, confirming three specific predictions: sovereignty-deficit behavior under electoral pressure; nonlinear legitimacy collapse triggering mass mobilization; and elite network preservation despite regime collapse, with an oligarchically connected prime minister appointed within weeks of the incumbent's ouster. From the equilibrium structure, we derive six general intervention principles— transformation islands— each targeting a specific parameter to alter the rules of the game. The findings extend beyond Madagascar to any fragile state where cohesive elite networks and external dependency jointly sustain predatory extraction across political transitions, as illustrated in Guinea-Bissau. Development failure in these states is not a coordination failure amenable to better policies within the existing game, but a stable strategic equilibrium that requires institutional engineering to alter the game's payoff structure.