  With respect to a $C^{\infty}$ metric which is close to the standard
Euclidean metric on $\mathbb{R}^{N+1+\ell}$, where $N\ge 7$ and $\ell\ge 1$ are
given, we construct a class of embedded $(N+\ell)$-dimensional hypersurfaces
(without boundary) which are minimal and strictly stable, and which have
singular set equal to an arbitrary preassigned closed subset
$K\subset\{0\}\times\mathbb{R}^{\ell}$.
