Let $X$ and $S$ $k$-schemes of finite type . ($k$ a field) and $U$ an open subset of $X$

Let $f:X\rightarrow S$ a $k$-morphism of finite type.

We assume that for any closed point $s\in S(\bar{k})$, $ U_{s}\neq\emptyset$, do we have that $U_{s}$ is non-empty for any $s\in S$?