  Let $f:\mathbb{K}^n\rightarrow\mathbb{K}^m$ be a generically finite
polynomial map of degree $d$ between affine spaces. In arXiv:1411.5011 we
proved that if $\mathbb{K}$ is the field of complex or real numbers, then the
set $S_f$ of points at which $f$ is not proper, is covered by polynomial curves
of degree at most $d-1$. In this paper we generalize this result to positive
characteristic. We provide a geometric proof of an upper bound by $d$.
