  Properties of the underlying-event in $pp$ interactions are investigated
primarily via the strange hadrons $K_{S}^{0}$, $\Lambda$ and $\bar\Lambda$, as
reconstructed using the ATLAS detector at the LHC in minimum-bias $pp$
collision data at $\sqrt{s} = 13$ TeV. The hadrons are reconstructed via the
identification of the displaced two-particle vertices corresponding to the
decay modes $K_{S}^{0}\rightarrow\pi^+\pi^-$, $\Lambda\rightarrow\pi^-p$ and
$\bar\Lambda\rightarrow\pi^+\bar{p}$. These are used in the construction of
underlying-event observables in azimuthal regions computed relative to the
leading charged-particle jet in the event. None of the hadronisation and
underlying-event physics models considered can describe the data over the full
kinematic range considered. Events with a leading charged-particle jet in the
range of $10 < p_T \leq 40$ GeV are studied using the number of prompt charged
particles in the transverse region. The ratio $N(\Lambda\rightarrow\pi^\mp
p^\pm)/N(K_{S}^{0}\rightarrow\pi^+\pi^-)$ as a function of the number of such
charged particles varies only slightly over this range. This disagrees with the
expectations of some of the considered Monte Carlo models.
