Fuzzy dark matter is an exciting alternative to the standard cold dark matter paradigm, reproducing its large scale predictions, while solving most of the existing tension with small scale observations. These models postulate that dark matter is constituted by light bosons and predict the condensation of a solitonic core-also known as boson star, supported by wave pressure-at the center of halos. However, solitons which host a parasitic supermassive black hole are doomed to be swallowed by their guest. It is thus crucial to understand in detail the accretion process. In this work, we use numerical relativity to self-consistently solve the problem of accretion of a boson star by a central black hole, in spherical symmetry. We identify three stages in the process, a boson quake, a catastrophic stage and a linear phase, as well as a general accurate expression for the lifetime of a boson star with an endoparasitic black hole. Lifetimes of these objects can be large enough to allow them to survive until the present time.