Yeah, that could definitely be a large square or rectangle that is pinned in the middle of one side (affixed near the top of the head) to create the smaller veil over the face. Doing that to a square or rectangle would cause it to fall like that.
Actually in the pipes:
- Remaking Ser Loras doublet.
- Luke Skywalker, A New Hope
- Wind Waker starter costume in swim material
Eventually: Paul from Dune, Faramir, Harry Sullivan