  Ground-based Imaging Cherenkov Telescope Arrays observe the Cherenkov
radiation emitted in extended atmospheric showers generated by cosmic gamma
rays in the TeV regime. The rate of these events is normally overwhelmed by 2-3
orders of magnitude more abundant cosmic rays induced showers. A large fraction
of these 'background' events is vetoed at the online trigger level, but a
substantial fraction still goes through data acquisition system and is saved
for the offline reconstruction. What kind of information those events carry,
normally rejected in the analysis? Is there the possibility that an exotic
signature is hidden in those data? In the contribution, some science cases, and
the problems related to the event reconstruction for the current and future
generation of these telescopes will be discussed.
