  We provide an example for stabilization by noise. Our approach does not rely
on monotonicity arguments due to the presence of higher order differential
operators or mixing properties of the system as the noise might be highly
degenerate. In the examples a scalar additive noise destroys a high-dimensional
random attractor of a PDE on an unbounded domain. In the presence of small
noise close to bifurcation all trajectories converge to a single stationary
solution.
