I was confused for a while when my first footman died because no one would pick up his loot. I later learned that you had to loot it. However, the game makes no indication of that. The items should appear outlined in red like any other loot drop item, so that the game lets players know they have to loot it manually.
there is an option to turn on auto loot, but yeah soldiers currently do not pick it up unless you pause the game and disable their job so that they do hauling only and then they will sometimes carry it back to base. I find it easiest to put chests where enemies usually attack so that they do not take as long to get back into a defensible area.