Peter, this is being used as a rim board for lateral support of joist.
Peter, I think Buddy had it pegged. It is hard to see the detail of what the boards do in your picture, but it appears the cut board is attached to the end of horizontal floor joists which are resting on the lower beam. The rim joist in this case would simply keep the floor joist from rotating.
Does this fit with what you saw on site? Do you have any more pictures?