I was wondering the same thing as Doug Floor Plan. Might it be a double-length sheet that functions as both the top sheet and the bottom sheet, with the fold at the foot end?

I share Doug's curiosity. The only theory that comes to mind is that perhaps a resident volunteers to wash a tablecloth that is used for church supper type functions.

but what is that long piece hanging behind the boys on the right? The light stripe in the weave makes it look like a tablecloth, but there's not a table that long in any of these units. It's hemmed. If it's a sheet or bedspread, it's for a single bed and still appears to be too long. Am I missing something obvious?

According to the Ghosts of DC website, Defrees Alley NE was located between I, K, North Capitol and First Streets. That area is now home to the Internal Revenue Service and the Federal Energy Regulatory Commission.