They don’t have to carry anything. If the media is involved, others (possibly even the media) will hand them not only the wood, but a knife and directions!
The media will help them.
Ok then they’ll be on the wrong side of the wall where they belong. And it would be a shame if they had a problem trying to return to the US cause thier passport was cancelled for attempting to aid and abet criminals crossing illegally. I can create hypotheticals too. :^)