  Background: Exclusive two-nucleon knockout after electroexcitation of nuclei
($A(e,e'NN)$ in brief) is considered to be a primary source of information
about short-range correlations (SRC) in nuclei. For a proper interpretation of
the data, final-state interactions (FSI) need to be theoretically controlled.
  Purpose: Our goal is to quantify the role of FSI effects in exclusive
$A(e,e'pN)$ reactions for four target nuclei representative for the whole mass
region. Our focus is on processes that are SRC driven. We investigate the role
of FSI for two characteristic detector setups corresponding with a "small" and
"large" coverage of the available phase space.
  Results: The transparency $T^{pN}_{A}$, defined as the ratio of exclusive
$(e,e'pN)$ cross sections on nuclei to those on "free" nucleon pairs, drops
from $ 0.2-0.3 $ for $^{12}$C to $0.04-0.07$ for $^{208}$Pb. For all considered
kinematics, the mass dependence of the $T^{pN}_{A}$ can be captured by the
power law $T^{pN}_{A} \propto A^{- \lambda}$ with $ 0.4 \lesssim \lambda
\lesssim 0.5 $. Apart from an overall reduction factor, we find that FSI only
modestly affects the distinct features of SRC-driven $A(e,e'pN)$ which are
dictated by the c.m. distribution of close-proximity pairs.
  Conclusion: The SCX mechanisms represent a relatively small (order of a few
percent) contribution of SRC-driven $A(e,e'pN)$ processes. The mass dependence
of FSI effects in exclusive $A(e,e'pN)$ can be captured in a robust power law
and is in agreement with the predictions obtained in a toy model.
