  The unavoidable interaction of quantum systems with their environment usually
results in the loss of desired quantum resources. Suitably chosen system
Hamiltonians, however, can, to some extent, counteract such detrimental decay,
giving rise to the set of stabilizable states. Here, we discuss the possibility
to stabilize Gaussian states in continuous-variable systems. We identify
necessary and sufficient conditions for such stabilizability and elaborate
these on two benchmark examples, a single, damped mode and two locally damped
modes. The obtained stabilizability conditions, which are formulated in terms
of the states' covariance matrices, are, more generally, also applicable to
non-Gaussian states, where they may similarly help to, e.g., discuss
entanglement preservation and/or detection up to the second moments.
