On icy bodies like the dwarf planet Ceres, impacts excavate volatile-rich material from beneath a dessicated lag layer and deposit it in the near-surface environment where higher temperatures drive sublimation. Ice has been detected in the upper meter of the ejecta blanket and interior of Occator crater, suggesting that large craters could be a significant source of exospheric water vapor. We assess the present-day exospheric contribution of a complex crater by first estimating the extent of volatile-rich deposits associated with a crater of a given size. We use a vapor diffusion model to calculate sublimation rates from the deposits, taking into account constraints on the thermophysical parameters of icy regolith from the Dawn mission. Extrapolating this model to craters formed throughout Ceres’ history, we find that the cumulative present-day sublimation rate from all complex crater deposits is ∼0.01 kg s−1, a factor of a few times greater than the outgassing rate from the global ice table. The dominant source of sublimation is not the conspicuous faculae but rather the volatile-rich ejecta blankets, which cover a significantly larger area than deposits in the crater interior. Because large impacts can blanket a significant fraction of the surface with ice-rich ejecta, complex craters are crucial for understanding the background present-day exosphere and the history of sublimation on icy bodies.