pelerine
A kind of short cape or covering for the shoulders, associated especially with medieval pilgrims (of any gender).
[…] Around his shoulders, he wore a thick gray pelerine. This was the custom of the knights of the Kingdom of the Spears, the land of the beaches and the chalk cliffs with great castles[…]
A woman's tippet or cape with long ends coming down in front.
Pilgrims, male or female, wore gowns […] A hood was usually added, but even if that were omitted, the pilgrim wore a shoulder-cape, a custom so universal that this type of cape came to be called a "pelerine," a name still used in the nineteenth century to describe the short capes fashionable in women's dress.
Where it comes from
Borrowed from French pèlerine, feminine of pèlerin (“pilgrim”), from Late Latin pelegrīnus. First attested in 1744.
Adapted from the Wiktionary entry pelerine (CC BY-SA 4.0).