  In the standard nearest-neighbor coarsening model with state space
$\{-1,+1\}^{\mathbb{Z}^2}$ and initial state chosen from symmetric product
measure, it is known (see~\cite{NNS}) that almost surely, every vertex flips
infinitely often. In this paper, we study the modified model in which a single
vertex is frozen to $+1$ for all time, and show that every other site still
flips infinitely often. The proof combines stochastic domination (attractivity)
and influence propagation arguments.
