Affine varieties/under geometric deformations/transcendental not affine, algebraic affine/Fakt

There is an example of a smooth projective (relatively over the affine line) variety ${}Z$ and an effective divisor ${}D\subset Z$ and a morphism

$Z\longrightarrow {\mathbb {A} }_{{\mathbb {F} }_{2}}^{1}$

such that ${}(Z\setminus D)_{\eta }$ is not an affine variety over the generic point ${}\eta$, but for every algebraic point ${}x$ the fiber ${}(Z\setminus D)_{x}$ is an affine variety.