Suppose $C$ is a complete algebraic curve.

Define a coherent locally free sheaf $\mathcal{F}$ over $C$ to be stable if $\mu(\mathcal{E})<\mu(\mathcal{F})$ for any subsheaf $\mathcal{E}$, where $\mu(\mathcal{E})=\text{deg}(\mathcal{E})/\text{rank}(\mathcal{E})$.

Suppose $\tilde{C}\to C$is a degree $d$ covering, I read about that the pull back of a semi-stable sheaf is semi-stable, but the case is not true for stable, is there any examples?

Thanks for comments and reference books!