In this work, we develop a rocky planet interior model and use it to investigate the evolution of catastrophically evaporating rocky exoplanets. These planets, detected through the dust tails produced by evaporative outflows from their molten surfaces, can be entirely destroyed in a fraction of their host star’s lifetime. To allow for the major decrease in mass, our interior model can simultaneously calculate the evolution of the pressure and density structure of a planet alongside its thermal evolution, which includes the effects of conduction, convection and partial melting. We first use this model to show that the underlying planets are likely to be almost entirely solid. This means that the dusty tails are made up of material sampled only from a thin dayside lava pool. If one wishes to infer the bulk compositions of rocky exoplanets from their dust tails, it is important to take the localized origin of this material into account. Secondly, by considering how frequently one should be able to detect mass loss from these systems, we investigate the occurrence of sub-Earth mass exoplanets, which is difficult with conventional planet detection surveys. We predict that, depending on model assumptions, the number of progenitors of the catastrophically evaporating planets is either in line with, or higher than, the observed population of close-in (substellar temperatures around 2200 K) terrestrial exoplanets.