  We present a numerical analysis of spin-$\frac{1}{2}$ fermions in a
one-dimensional harmonic potential in the presence of a magnetic point-like
impurity at the center of the trap. The model represents a few-body analogue of
a magnetic impurity in the vicinity of an $s$-wave superconductor. Already for
a few particles we find a ground-state level crossing between sectors with
different fermion parities. We interpret this crossing as a few-body precursor
of a quantum phase transition, which occurs when the impurity `breaks' a Cooper
pair. This picture is further corroborated by analyzing density-density
correlations in momentum space. Finally, we discuss how the system may be
realized with existing cold-atoms platforms.
