  Landau suggested that the low-temperature properties of metals can be
understood in terms of long-lived quasiparticles with all complex interactions
included in Fermi-liquid parameters, such as the effective mass $m^{\star}$.
Despite its wide applicability, electronic transport in bad or strange metals
and unconventional superconductors is controversially discussed towards a
possible collapse of the quasiparticle concept. Here we explore the
electrodynamic response of correlated metals at half filling for varying
correlation strength upon approaching a Mott insulator. We reveal persistent
Fermi-liquid behavior with pronounced quadratic dependences of the optical
scattering rate on temperature and frequency, along with a puzzling elastic
contribution to relaxation. The strong increase of the resistivity beyond the
Ioffe-Regel-Mott limit is accompanied by a `displaced Drude peak' in the
optical conductivity. Our results, supported by a theoretical model for the
optical response, demonstrate the emergence of a bad metal from resilient
quasiparticles that are subject to dynamical localization and dissolve near the
Mott transition.
