The Regency Wardrobe Collection - research & making - Wrapped in birds and butterflies
A standard accessory during the Regency, for any modest woman who felt she would otherwise have too much cleavage on show was a fichu, also called a “tucker” for you tucked it into the bodice of your gown.
Fichus from the 3rd quarter of the 18th century and 1789
The Met Museum
"Fichu - softly draped collar" - The Regency by Marion Sichel
"A fichu is a large, square kerchief worn by women to fill in the low neckline of a bodice. It originated in the United Kingdom in the 18th century and remained popular there and in France through the 19th with many variations as well as in the United States. The fichu was generally of linen fabric and was folded diagonally into a triangle and tied, pinned, or tucked into the bodice in front." - Wikipedia
"Fichu was, broadly speaking, the French term for a neckerchief or scarf. The term appears in French from at least as early as the mid-18th century, and was adopted for English use as a more elegant alternative to neckerchief in the early 19th century."
For more about the differences between Handkerchiefs, Neckerchiefs, Buffons (in French the Fichu Menteur) and Fichus see: http://thedreamstress.com/2013/05/terminology-buffons-fichu-neckerchief-handkerchief/
18th-19th Century - The Met Museum
Triangular Fichu early 19th Century https://www.meg-andrews.com/item-details/Triangular-Fichu/7514
1805-1810 - The V&A
"This antique blonde lace tambour embroidered fichu...dates from 1830. It is hand stitched, made of a sheer fine off white blonde net lace, with tambour embroidery work chain stitching done in a floral spray vine leaf pattern design. It features long lappet front ends which could be crossed at the front, tied in the back and would have been worn for modesty" - https://www.1860-1960.com/xa7596p0.html