Decentralized protocols claim immutable, rule-based execution, yet many embed emergency mechanisms such as chain-level freezes, protocol pauses, and account quarantines. These overrides are crucial for responding to exploits and systemic failures, but they expose a core tension: when does intervention preserve trust and when is it perceived as illegitimate discretion? With approximately $10$ billion in technical exploit losses potentially addressable by onchain intervention (2016--2026), the design of these mechanisms has high practical stakes, but current approaches remain ad hoc and ideologically charged. We address this gap by developing a Scope $\times$ Authority taxonomy that maps the design space of emergency architectures along two dimensions: the precision of the intervention and the concentration of trigger authority. We formalize the resulting tradeoffs of a standing centralization cost versus containment speed and collateral disruption as a stochastic cost-minimization problem; and derive three testable predictions. Assessing these predictions against 705 documented exploit incidents, we find that containment time varies systematically by authority type; that losses follow a heavy-tailed distribution ($α\approx 1.33$) concentrating risk in rare catastrophic events; and that community sentiment measurably modulates the effective cost of maintaining intervention capability. The analysis yields concrete design principles that move emergency governance from ideological debate towards quantitative engineering.