  The ANtarctic Impulsive Transient Antenna (ANITA) collaboration has observed
two EeV-energy, upward going events originating from below the horizon. As no
standard model (SM) particles, propagating through the earth at such energy and
exit angles, can give rise to the required survival probability for the
observed events, several beyond standard model (BSM) proposals have come up. We
propose a scenario where a $Z_2$ odd sector is responsible for such anomalous
events. The next to lightest $Z_2$ odd particle or the next to lightest stable
particle (NLSP), created from ultra high energy neutrino interactions with
nucleons, can pass through the earth and then decay into the lightest $Z_2$ odd
particle or the lightest stable particle (LSP) and a tau lepton. The long-lived
nature of the NLSP requires its coupling with the LSP to be very small, keeping
the LSP out of thermal equilibrium in the early universe. The LSP can then be a
non-thermal dark matter while the tau leptons produced from NLSP decay after
passing through the earth can explain the ANITA events. We first show that a
purely non-thermal dark matter scenario can not give rise to the required event
rates while a hybrid scenario where dark matter can have both thermal as a well
non-thermal contribution to its relic abundance, serves the purpose.
