Recent studies of the Λ(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 πΣ∗(1385) in this case, although the coupling of the Λ(1520) to the K¯N and πΣ makes this picture only approximate. The πΣ∗(1385) decay channel of the Λ(1520) is forbidden in free space for the nominal mass of the Σ∗(1385), but the coupling of the π to ph components in the nuclear medium opens new decay channels of the Λ(1520) in the nucleus and produces a much larger width. Together with medium modifications of the K¯N and πΣ decay channels, the final width of the Λ(1520) at nuclear matter density is more than five times bigger than the free one. We perform the calculations by dressing simultaneously the Λ(1520) and the Σ∗(1385) resonances, finding moderate changes in the mass but substantial ones in the width of both resonances.