  Recent studies of the $\Lambda(1520)$ resonance within chiral unitary theory
with coupled channels find the resonance as a dynamically generated state from
the interaction of the decuplet of baryons and the octet of mesons, essentially
a quasibound state of $\pi \Sigma^*(1385)$ in this case, although the coupling
of the $\Lambda(1520)$ to the $\bar{K}N$ and $\pi \Sigma$ makes this picture
only approximate. The $\pi \Sigma^*(1385)$ decay channel of the $\Lambda(1520)$
is forbidden in free space for the nominal mass of the $\Sigma^*(1385)$, but
the coupling of the $\pi$ to $ph$ components in the nuclear medium opens new
decay channels of the $\Lambda(1520)$ in the nucleus and produces a much larger
width. Together with medium modifications of the $\bar{K}N$ and $\pi \Sigma$
decay channels, the final width of the $\Lambda(1520)$ at nuclear matter
density is more than five times bigger than the free one. We perform the
calculations by dressing simultaneously the $\Lambda(1520)$ and the
$\Sigma^*(1385)$ resonances, finding moderate changes in the mass but
substantial ones in the width of both resonances.
