  Single star evolution does not allow extremely low-mass stars to cross the
classical instability strip (IS) during the Hubble time. However, within binary
evolution framework low-mass stars can appear inside the IS once the mass
transfer (MT) is taken into account. Triggered by a discovery of low-mass 0.26
Msun RR Lyrae-like variable in a binary system, OGLE-BLG-RRLYR-02792, we
investigate the occurrence of similar binary components in the IS, which set up
a new class of low-mass pulsators. They are referred to as Binary Evolution
Pulsators (BEPs) to underline the interaction between components, which is
crucial for substantial mass loss prior to the IS entrance. We simulate a
population of 500 000 metal-rich binaries and report that 28 143 components of
binary systems experience severe MT (loosing up to 90% of mass), followed by at
least one IS crossing in luminosity range of RR Lyrae (RRL) or Cepheid
variables. A half of these systems enter the IS before the age of 4 Gyr. BEPs
display a variety of physical and orbital parameters, with the most important
being the BEP mass in range 0.2-0.8 Msun, and the orbital period in range
10-2500 d. Based on the light curve only, BEPs can be misclassified as genuine
classical pulsators, and as such they would contaminate genuine RRL and
classical Cepheid variables at levels of 0.8% and 5%, respectively. We state
that the majority of BEPs will remain undetected and we discuss relevant
detection limitations.
