  We explore non-unitary dynamics of $2+1$ dimensional free fermions and show
that the obtained steady state is critical regardless the strength of the
non-unitary evolution. Numerical results indicate that the entanglement entropy
has a logarithmic violation of the area-law and the mutual information between
two distant regions decays as a power-law function. In particular, we provide
an interpretation of these scaling behaviors in terms of a simple
quasi-particle pair picture. In addition, we study the dynamics of the
correlation function and demonstrate that this system has dynamical exponent
$z=1$. We argue the dynamics of the correlation function in terms of a
classical non-linear master equation. Our method opens a door to a vast number
of non-unitary random dynamics in free fermions and can be generalized to any
dimensions.
