Plants with extremely shallow roots that grow in shade?

I have a townhome with a fenced-in patio/garden area that I moved into last fall. The garden was basically a bunch of weeds (I don't think the previous owner did anything), except for one area what was only dirt. The area is in full shade due to being in a south-facing corner and under the tree in my garden. I set out to beautify the area with some plants that grow in shade. But when I began digging, I hit concrete. I soon discovered that area (about 4x3 ft) is an old sidewalk from when the building was constructed in the 40s and is only about 2-3 inches below the level of the newer patio, and because of that was silted in with dirt but too shallow for plants to take root. I live in Indiana, byu the way, so all seasons are experienced. I thought about filling the area with river stones and making a small rock garden, but figure the rocks would soon be filled in with dirt through a year of rain (not to mention how to remove the leaves and seed pods that fall from the tree above it). My question: Are there any plants (perhaps are ground ivy or other ground cover) that will survive and thrive under such shallow, low light conditions in my climate? Or does anyone have suggestions on what to do with the area?