The colossal seated statue of Abraham Lincoln (by Daniel Chester French, 1920) in the Lincoln Memorial has an American flag draped over the back of the chair—specifically, a 36-star Union flag representing the states at the time of Lincoln’s death (1865).
The flag is a permanent sculpted element (Georgia marble), not textile. It symbolizes the Union he preserved. The chair’s fasces (bundled rods) on the arms represent federal authority; the open hands signify reconciliation.