The pretty housemaid corset was a Symington design and one of the things that I read about Symington corded panels was that the cording used was twisted paper. Depending upon the final application the cording could have been composed of up to 3 layers of paper. The paper went through a water bath, was twisted, and then sewn between two layers of cloth in a long continuous loop. Some of the machines described had six needles; could sew corded panels with 6, 12, or 18 rows of cording since the strip was a continuous loop. The loop was then steam dried and the cotton would shrink around the paper cording. Corded panels were then cut and used in the corset.
If you think paper cord is a strange material to use you haven't seen high quality paper cord. Single layer tightly twisted paper cord is extremely strong.
There was a museum publication about the Symington Collection and this bit about the cording appeared in the publication with a picture of the cording being sewn.