About midway between the northern and southern boundaries of Concordia the cemetery is interrupted by two narrow strips of land, about 100 feet wide, that project inwards from the eastern and western edges, nearly touching in the center. These areas are protected by a fence and not accessible from Concordia; one is a parking lot, the other, an empty and open grassy space. In the narrow space between these two areas, a passage leads from the north to the south sections of Concordia.

Before the construction of the Eisenhower expressway, a CTA train line passed through Concordia at this point, serving all of the cemeteries in this area - Concordia, Forest Home, Jewish Waldheim. When the expressway was constructed the train line was moved, and the station and tracks removed. The CTA continues to use part of the property - just east of Concordia is a maintenance yard - but has simply fenced off the area where the track was within Concordia, and the land is currently unused.