  With assumptions that the violation of the distance-duality (DD) relation
entirely arises from non-conservation of the photon number and the absorption
is frequency independent in the observed frequency range, we perform
cosmological-model-independent tests for the cosmic opacity. The observational
data include the largest Union2.1 SN Ia sample, which is taken for observed
$D_\mathrm{L}$, and galaxy cluster samples compiled by De Filippis {\it et al.}
and Bonamente {\it et al.}, which are responsible for providing observed
$D_\mathrm{A}$. Two parameterizations, $\tau(z)=2\epsilon z$ and
$\tau(z)=(1+z)^{2\epsilon}-1$ are adopted for the optical depth associated to
the cosmic absorption. We find that, an almost transparent universe is favored
by Filippis {\it et al.} sample but it is only marginally accommodated by
Bonomente {\it et al.} samples at 95.4% confidence level (C. L.) (even at 99.7%
C. L. when the $r<100 \mathrm{kpc}$-cut spherical $\beta$ model is considered).
Taking the possible cosmic absorption (in 68.3% C. L. range) constrained from
the model-independent tests into consideration, we correct the distance modulus
of SNe Ia and then use them to study their cosmological implications. The
constraints on the $\Lambda$CDM show that a decelerating expanding universe
with $\Omega_\Lambda=0$ is only allowed at 99.7% C. L. by observations when the
Bonamente {\it et al.} sample is considered. Therefore, our analysis suggests
that an accelerated cosmic expansion is still needed to account for the dimming
of SNe and the standard cosmological scenario remains to be supported by
current observations.
