  The Little Sibling of the Big Rip is a cosmological abrupt event predicted by
some phantom cosmological models that could describe our Universe. When this
event is approached the observable Universe and its expansion rate grow
infinitely, but its cosmic derivative remains finite. In this work we have
obtained the group of metric $f(R)$ theories of gravity that reproduce this
classical cosmological background evolution. Furthermore, we have considered
the quantization of some of the resulting models in the framework of quantum
geometrodynamics, showing that the DeWitt criterion can be satisfied.
Therefore, as it also happens in General Relativity, this event may be avoided
in $f(R)$ quantum cosmology.
