  We demonstrate how holonomy corrections in loop quantum cosmology (LQC)
prevent the Big Rip singularity by introducing a quadratic modification in
terms of the energy density $\rho$ in the Friedmann equation in the
Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) space-time in a consistent and
useful way. In addition, we investigate whether other kind of singularities
like Type II,III and IV singularities survive or are avoided in LQC when the
universe is filled by a barotropic fluid with the state equation
$P=-\rho-f(\rho)$, where $P$ is the pressure and $f(\rho)$ a function of
$\rho$. It is shown that the Little Rip cosmology does not happen in LQC.
Nevertheless, the occurrence of the Pseudo-Rip cosmology, in which the phantom
universe approaches the de Sitter one asymptotically, is established, and the
corresponding example is presented. It is interesting that the disintegration
of bound structures in the Pseudo-Rip cosmology in LQC always takes more time
than that in Einstein cosmology. Our investigation on future singularities is
generalized to that in modified teleparallel gravity, where LQC and Brane
Cosmology in the Randall-Sundrum scenario are the best examples. It is
remarkable that $F(T)$ gravity may lead to all the kinds of future
singularities including Little Rip.
