According to Mr. Cambell the author of the the London Tradesman, this is the Division of Work in the shop of the Stay-Maker:
The Stay-Maker takes the ladies shape as nicely as he can, cuts out the tabby and canvas which is then given to women to sew the rows of stitching. This is piece work and the pay is minimal. Anyone who has examined a pair of original and professionally made stays can bear witness to the perfection of stitching and the many hours of labor required to sew all of the channels for a pair of stays.
Proceedings of the Old Bailey,Samuel Lowe, Susanah Butcher, Theft 4th December 1751.
“I have known her three years, she lived with me about 2 years ago; I never heard any thing, but what she is a very honest girl; her business is stitching of stays.”
Stay binding, trimming, and whale fin were purchased from the Haberdasher and then the job of stuffing the whale fin into the channels was done by the Master or Foreman of the shop.
"The work is too hard for Women, it requires more strength than they are capable of.." London Tradesman, c1747
The stays were then loosely sewn together, taken to the customer for a final fitting and then they were finished by laying braid along the seam and lacing across the stomacher and the edges bound.