  Near the tip of the stau coannihilation strip in the CMSSM with a neutralino
LSP, the astrophysical cold dark matter density constraint forces the
stau-neutralino mass difference to be small. If this mass difference is smaller
than the tau mass, the stau may decay either in the outer part of an LHC
detector - the `disappearing track' signature - or be sufficiently long-lived
to leave the detector before decaying - the long-lived massive charged-particle
signature. We combine searches for these signatures with conventional missing
transverse energy searches during LHC Run 1, identifying the small remaining
parts of the CMSSM stau coannihilation strip region that have not yet been
excluded, and discussing how they may be explored during Run 2 of the LHC.
