Neutron-rich $^{119}\mathrm{Pd}$ 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 $^{119}\mathrm{Pd}$. Their ${\ensuremath{\beta}}^{\ensuremath{-}}$ decay was measured with $\ensuremath{\gamma}\ensuremath{\gamma}$- and $\ensuremath{\beta}\ensuremath{\gamma}$-spectroscopy methods using low-energy germanium detectors and a thin plastic scintillator. Two distinct nuclear-level structures were observed in $^{119}\mathrm{Ag}$, based on the $1/{2}^{\ensuremath{-}}$ and $7/{2}^{+}$ isomers reported previously. The ${\ensuremath{\beta}}^{\ensuremath{-}}$-decay work was complemented by a prompt-$\ensuremath{\gamma}$ study of levels in $^{119}\mathrm{Ag}$ populated in spontaneous fission of $^{252}\mathrm{Cf}$, performed using the Gammasphere array of germanium detectors. Contrary to previous suggestions, our data show that the $1/{2}^{\ensuremath{-}}$ isomer is located below the $7/{2}^{+}$ isomer and is proposed as a new ground state of $^{119}\mathrm{Ag}$ with the $7/{2}^{+}$ isomer excitation energy determined to be 33.4 keV. Our data indicate that there are two $\ensuremath{\beta}$ unstable isomers in $^{119}\mathrm{Pd}$, a proposed ground state of $^{119}\mathrm{Pd}$ 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 ($11/{2}^{\ensuremath{-}}$) 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 $\ensuremath{\gamma}$ cascade comprising 18.7-219.8-$\mathrm{X}$-keV transitions. The unobserved isomeric transition with energy $X\ensuremath{\approx}100$ 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 $^{119}\mathrm{Pd}$. Oblate configurations in $^{119}\mathrm{Ag}$ are discussed also.