I ran into the following statement in a talk. Assume we are in characteristic zero. Let $X$ be an smooth affine variety, let $X\to Z$ be an open immersion with dense image, such that $Z$ is smooth and proper, and $Z-X$ is a normal crossings divisor. Then if we have an etale map $Y\to X$, there is an extension $Y'\to Z$.
I can't find a proof of this fact. When I asked the speaker, he said that it is in SGA, but that doesn't really narrow down the search.