The square shawl is not part of the Chinese dress tradition. It was a popular shape in Europe, where ladies both wore square shawls and used them in interior decoration.They draped them over pianos and tables and pinned them on walls.
In the workshops, specialised weavers must have set up the very wide looms needed to produce the roughly square seam-free pieces of silk. In Britain, these fringed silk shawls were popular from about 1840 to1910 because they were seen as 'artistic' and bohemian rather than as mainstream fashion accessories.