Let $N$ be a hyperbolic 3-manifold and $B$ a component of the interior of $AH(\pi _1(N))$, the space of marked hyperbolic 3-manifolds homotopy equivalent to $N$. We will give topological conditions on $N$ sufficient to give $\rho \in \bar{B}$ such that for every sufficiently small neighbourhood $V$ of $\rho$, $V\cap B$ is disconnected. This implies that $\bar{B}$ is not a manifold with boundary.