  In this paper we study the irreducible components of the compactified
Jacobian of a ribbon $X$ of arithmetic genus $g$ over a smooth curve
$X_{\mathrm{red}}$ of genus $\bar{g}$. We prove that when $g\geq 4\bar{g}-2$
the moduli space of rank $2$ semistable vector bundles over $X_{\mathrm{red}}$
is not an irreducible component and we determine the irreducible components in
which it is contained. This answers a question of D. Chen and J.L. Kass in [CK]
and completes their results.
