  We present STAR measurements of strange hadron ($\mathrm{K}^{0}_{\mathrm S}$,
$\Lambda$, $\overline{\Lambda}$, $\Xi^-$, $\overline{\Xi}^+$, $\Omega^-$,
$\overline{\Omega}^+$, and $\phi$) production at mid-rapidity ($|y| < 0.5$) in
Au+Au collisions at $\sqrt{s_{_{\mathrm{NN}}}}$ = 7.7 - 39 GeV from the Beam
Energy Scan Program at the Relativistic Heavy Ion Collider (RHIC). Transverse
momentum spectra, averaged transverse mass, and the overall integrated yields
of these strange hadrons are presented versus the centrality and collision
energy. Antibaryon-to-baryon ratios ($\overline{\Lambda}$/$\Lambda$,
$\overline{\Xi}^+$/$\Xi^-$, $\overline{\Omega}^+$/$\Omega^-$) are presented as
well, and used to test a thermal statistical model and to extract the
temperature normalized strangeness and baryon chemical potentials at hadronic
freeze-out ($\mu_{B}/T_{\rm ch}$ and $\mu_{S}/T_{\rm ch}$) in central
collisions. Strange baryon-to-pion ratios are compared to various model
predictions in central collisions for all energies. The nuclear modification
factors ($R_{\textrm{CP}}$) and antibaryon-to-meson ratios as a function of
transverse momentum are presented for all collision energies. The
$\mathrm{K}^{0}_{\mathrm S}$ $R_{\textrm{CP}}$ shows no suppression for $p_{\rm
T}$ up to 3.5 $\mathrm{GeV} / c$ at energies of 7.7 and 11.5 GeV. The
$\overline{\Lambda}$/$\mathrm{K}^{0}_{\mathrm S}$ ratio also shows
baryon-to-meson enhancement at intermediate $p_{\rm T}$ ($\approx$2.5
$\mathrm{GeV} / c$) in central collisions at energies above 19.6 GeV. Both
observations suggest that there is likely a change of the underlying strange
quark dynamics at collision energies below 19.6 GeV.
