  Let $C$ be a chain-like curve having $n$ smooth components and $n-1$ nodes,
where $n \geq 2$. Let $E$ be a vector bundle on $C$ and $V \subseteq H^0(E)$ be
a linear subspace generating $E$. We investigate the (semi)stability of the
kernel bundle $M_{E,V}$ associated to $(E,V)$.
