  We study a linear rotor in a bosonic bath within the angulon formalism. Our
focus is on systems where isotropic or anisotropic impurity-boson interactions
support a shallow bound state. To study the fate of the angulon in the vicinity
of bound-state formation, we formulate a beyond-linear-coupling angulon
Hamiltonian. First, we use it to study attractive, spherically symmetric
impurity-boson interactions for which the linear rotor can be mapped onto a
static impurity. The well-known polaron formalism provides an adequate
description in this limit. Second, we consider anisotropic potentials, and show
that the presence of a shallow bound state with pronounced anisotropic
character leads to a many-body instability that washes out the angulon
dynamics.
