  Let $M^{n+1}$ be a closed manifold of dimension $3\leq n+1\leq 7$. We show
that for a $C^\infty$-generic metric $g$ on $M$, to any connected, closed,
embedded, $2$-sided, stable, minimal hypersurface $S\subset (M,g)$ corresponds
a sequence of closed, embedded, minimal hypersurfaces $\{\Sigma_k\}$ scarring
along $S$, in the sense that the area and Morse index of $\Sigma_k$ both
diverge to infinity and, when properly renormalized, $\Sigma_k$ converges to
$S$ as varifolds. We also show that scarring of immersed minimal surfaces along
stable surfaces occurs in most closed Riemannian $3$-manifods.
