  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 \emph{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 {\it boson-quake}, a {\it 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.
