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Stars falling too close to massive black holes in the centers of galaxies can be torn apart by the strong tidal forces. Simulating the subsequent feeding of the black hole with disrupted material has proved challenging because of the range of timescales involved. Here we report a set of simulations that capture the relativistic disruption of the star, followed by 1 yr of evolution of the returning debris stream. These reveal the formation of an expanding asymmetric bubble of material extending to hundreds of au—an outflowing Eddington envelope with an optically thick inner region. Such outflows have been hypothesized as the reprocessing layer needed to explain optical/UV emission in tidal disruption events but never produced self-consistently in a simulation. Our model broadly matches the observed light curves with low temperatures, faint luminosities, and line widths of 10,000–20,000 km s ^−1 .