Neutron-rich $^{119}$Pd nuclei were produced in fission of natural uranium, induced by 25-MeV protons. Fission fragments swiftly extracted with the Ion Guide Isotope Separation On-Line method were mass separated using a dipole magnet and a Penning trap, providing mono-isotopic samples of $^{119}$Pd. Their $\beta^-$ decay was measured with $\gamma \gamma$- and $\beta \gamma$-spectroscopy methods using low-energy germanium detectors and a thin plastic scintillator. Two distinct nuclear-level structures were observed in $^{119}$Ag, based on the $1/2^-$ and $7/2^+$ isomers reported previously. The $\beta^-$-decay work was complemented by a prompt-γ study of levels in $^{119}$Ag populated in spontaneous fission of $^{252}$Cf, performed using the Gammasphere array of germanium detectors. Contrary to previous suggestions, our data show that the $1/2^-$ isomer is located below the $7/2^+$ isomer and is proposed as a new ground state of $^{119}$Ag with the $7/2^+$ isomer excitation energy determined to be 33.4 keV. Our data indicate that there are two β unstable isomers in $^{119}$Pd, a proposed ground state of $^{119}$Pd with tentative spin $1/2^+$ or $3/2^+$ and a half-life of 0.88 s and the other one about 350 keV above, having spin $(11/2^-)$ and a half-life of 0.85 s. The higher-energy isomer probably decays to the $1/2^+$ or $3/2^+$ ground state via a $\gamma$ cascade comprising 18.7-219.8-X-keV transitions. The unobserved isomeric transition with energy X ≈ 100 keV probably has an E3 multipolarity. Its hindrance factor is significantly lower than for analogous E3 isomeric transitions in lighter Pd isotopes, suggesting an oblate deformation of levels in  $^{119}$Pd. Oblate configurations in  $^{119}$Ag are discussed also.< Réduire