  We study the IR phases of 3D class R theories associated with closed
non-hyperbolic 3-manifolds. Non-hyperbolic 3-manifolds can be obtained by
performing Dehn fillings on 1-cusped hyperbolic 3-manifolds along exceptional
slopes. In 3D-3D correspondence, the `exceptional' Dehn filling corresponds to
the gauging of an $SU(2)$ flavor symmetry in a superconformal field theory
associated with a 1-cusped 3-manifold with `small' Chern-Simons levels. With
several explicit examples, we analyze various interesting non-perturbative IR
phenomena (such as spontaneous SUSY breaking, generation of mass gap and
supersymmetry enhancement) from the `exceptional' gaugings. Interestingly,
distinguished features of the IR phases can be captured by simple topological
properties of non-hyperbolic 3-manifolds. We also find that 3D class R theories
associated with certain classes of atoroidal non-hyperbolic 3-manifolds always
exhibit supersymmetry enhancement at low energy and actually flow to 3D rank-0
$\mathcal{N}=4$ SCFTs with trivial vacuum moduli space.
