  Natural supersymmetry (SUSY) with light higgsinos is perhaps the most
plausible of all weak scale SUSY models while a variety of motivations point to
(right) tau sleptons as the lightest of all the sleptons. We examine a SUSY
model line with rather light right-staus embedded within natural SUSY. For
light stau_1 of a few hundred GeV, then the decays stau_1 -> \tau\tchi_{1,2}^0
and \nu_\tau\tchi_1^- occur at comparable rates where the (higgsino-like)
\tchi_1^\pm and \tchi_2^0 release only small visible energy: in this case, the
expected \tau^+\tau^- +\eslt signature is diminished from usual expectations
due to the presence of the nearly invisible decay mode \ttau_1 ->
\nu_\tau\tchi_1^-. However, once m_{\ttau_1}> ~m(bino), then decays to binos
such as \ttau_1 -> \tau\tchi_3^0 open up where \tchi_3^0 decays to higgsinos
plus W^\pm, Z^0 and h at comparable rates. For these heavier staus, then stau
pair production gives rise to diboson+\eslt events which may contain 0, 1 or 2
additional hard \tau leptons. From these considerations, we examine the
potential for future discovery of tau-slepton pair production at
high-luminosity LHC. While we do not find a 5\sigma HL-LHC discovery reach for
3000 fb^{-1}, we do find a 95\% CL exclusion reach, ranging between
m_{\ttau_1}:100-450 GeV for m_{\tchi_1^0}~ 100 GeV. This latter reach
disappears for m_{\tchi_1^0}>~ 200 GeV.
