Let $X$ a smooth projective connected curve over $\mathbb{C}$. Let $E$ a vector bundle and $E'$ a subbundle of $E$. Let $(x_{1},\dots,x_{n})$ $n$ closed points on the curve $X$ with $n>2g$ and $z$ an auxiliary closed point. Can we find for all $m\geq 0$, a section $f\in H^{0}(X,E\otimes O_{X}(D_{m}))$

with $D_{m}=[x_{1}]+\dots+[x_{n}]+m[z]$ such that at the points $x_{1},\dots,x_{n}$ the section $f$ factorizes through the subbundle $E'$?