  Contracting cosmologies are known to be flawed with a shear instability,
where the contribution from the anisotropic stress to the overall energy
density grows as $a^{-6}$, with $a$ the scale factor. Classically, whether or
not this contribution becomes important before the bounce depends on its
initial value, which can always be sufficiently fine tuned to make it
irrelevant. However, vacuum quantum fluctuations inevitably provide a
non-vanishing source of anisotropic stress. In this work, we compute the
minimum amount of shear that is obtained if one assumes that it vanishes
initially, but lets quantum fluctuations build it up. In practice, we consider
a massless test scalar field, and describe its quantum fluctuations by means of
the stochastic "inflation" (though here applied to a contracting phase)
formalism. We find that, if the equation-of-state parameter of the contraction
satisfies $w>-1/9$, regardless of when the contracting phase is initiated, the
time at which the shear becomes sizeable is always when the Hubble scale
approaches the Planck mass (which is also where the bounce is expected to take
place). However, if $w<-1/9$, the shear backreaction becomes important much
earlier, at a point that depends on the overall amount of contraction.
