  The stau-neutralino coannihilation provides a feasible way to accommodate the
observed cosmological dark matter (DM) relic density in the minimal
supersymmetric standard model (MSSM). In such a coannihilation mechanism the
stau mass usually has an upper bound since its annihilation rate becomes small
with the increase of DM mass. Inspired by this observation, we examine the
upper limit of stau mass in the parameter space with a large mixing of staus.
We find that the stau pair may dominantly annihilate into dibosons and hence
the upper bound on the stau mass ($\sim400$ GeV) obtained from the $f\bar{f}$
final states can be relaxed. Imposing the DM relic density constraint and
requiring a long lifetime of the present vacuum, we find that the lighter stau
mass can be as heavy as about 1.4 TeV for the stau maximum mixing. However, if
requiring the present vacuum to survive during the thermal history of the
universe, this mass limit will reduce to about 0.9 TeV. We also discuss the
complementarity of vacuum stability and direct detections in probing this stau
coannihilation scenario.
