  Future $c$-$\tau$ factories are natural places to study extensions of the
Standard Model of particle physics (SM) with new long-lived feebly interacting
particles light enough to be produced in electron-positron collisions. We
investigate prospects of these machines in exploring such extensions
emphasizing the role of polarized beams in getting rid of the SM irreducible
background for the missing energy signature. We illustrate this on example of
$c$-$\tau$ project in Novosibirsk, where the electron beam is designed to be
polarized to achieve much higher sensitivity to hadronic resonances and
$\tau$-leptons. We investigate models with hidden photons, with millicharged
particles (fermions and scalars), with $Z'$ bosons and with axion-like
particles. We find that the electron beam polarization of 80\% significantly
improves the chances to observe the signal, especially with large statistics.
We outline the regions of the model parameter space which can be reached at
this factory in one year and in ten years of operation according with the
scientific schedule of tuning the energy of colliding beams.
