We show that strong molecular rotation drastically modifies the autodetachment of C_{2}^{-} ions in the lowest quartet electronic state a^{4}Σ_{u}^{+}. In the strong-rotation regime, levels of this state only decay by a process termed "rotationally assisted" autodetachment, whose theoretical description is worked out based on the nonlocal resonance model. For autodetachment linked with the exchange of six rotational quanta, the results reproduce a prominent, hitherto unexplained electron emission signal with a mean decay time near 3 ms, observed on stored C_{2}^{-} ions from a hot ion source.