  Using analytical and path integral Monte Carlo methods, we study the
susceptibility $\chi_{dc}(T)$ of a spin-S impurity with XY rotational symmetry
embedded in a metal. Close to a ferromagnetic quantum critical point, the
impurity polarizes conduction electrons in its vicinity and forms a large
magnetic droplet with moment M>>S. At not too low temperatures, the strongly
damping paramagnon modes of the conduction electrons suppress large quantum
fluctuations (or spin flips) of this droplet. We show that the susceptibility
follows the law $\chi_{dc}(T)=(M^{2}/T)[1-(\pi g)^{-1}\ln(gE_{0}/T)]$, where
the parameter g>>1 describes the strong damping by conduction electrons, and
E_0 is the bandwidth of paramagnon modes. At exponentially low temperatures T
<< T_{*} ~ E_{0}\exp(-\pi g/2) we show that spin flips cannot be ignored. In
this regime we find that $\chi_{dc}(T) \approx \chi_{dc}(0)
[1-(2/3)(T/T_{*})^2]$, where $\chi_{dc}(0)\sim M^{2}/T_{*}$ is finite and
exponentially large in g. We also discuss these effects in the context of the
multi-channel Kondo impurity model.
