  The first search for supersymmetry in events with an experimental signature
of one soft, hadronically decaying $\tau$ lepton, one energetic jet from
initial-state radiation, and large transverse momentum imbalance is presented.
These event signatures are consistent with direct or indirect production of
scalar $\tau$ leptons ($\tilde{\tau}$) in supersymmetric models that exhibit
coannihilation between the $\tilde{\tau}$ and the lightest neutralino
($\tilde{\chi}^0_1$), and that could generate the observed relic density of
dark matter. The data correspond to an integrated luminosity of 77.2 fb$^{-1}$
of proton-proton collisions at $\sqrt{s} =$ 13 TeV collected with the CMS
detector at the LHC in 2016 and 2017. The results are interpreted in a
supersymmetric scenario with a small mass difference ($\Delta m$) between the
chargino ($\tilde{\chi}^\pm_1$) or next-to-lightest neutralino
($\tilde{\chi}^0_2$), and the $\tilde{\chi}^0_1$. The mass of the
$\tilde{\tau}$ is assumed to be the average of the $\tilde{\chi}^\pm_1$ and
$\tilde{\chi}^0_1$ masses. The data are consistent with standard model
background predictions. Upper limits at 95% confidence level are set on the sum
of the $\tilde{\chi}^\pm_1$, $\tilde{\chi}^0_2$, and $\tilde{\tau}$ production
cross sections for $\Delta m(\tilde{\chi}^\pm_1, \tilde{\chi}^0_1) =$ 50 GeV,
resulting in a lower limit of 290 GeV on the mass of the $\tilde{\chi}^\pm_1$,
which is the most stringent to date and surpasses the bounds from the LEP
experiments.
