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Shawl.
I think you are talking about the stole (long rectangular scarf)
The garment worn over the shoulders is spelt shawl.
shawl
The homophone of shall is shawl, which is a kind of wrap or garment worn around the shoulders.
She wrapped a cozy shawl around her shoulders as she watched the sunset from the porch.
The brightly colored shawl commonly worn in Latin America is known as a "rebozo." It is a traditional garment that is draped over the shoulders and can be used for various purposes such as keeping warm, carrying goods, or as a fashion accessory.
a sash, a shoulder sash shawl, ruana,serape,cape or capelet,stole,shrug
I believe it is called, a shawl.
shawl
Your shawl is on the kitchen counter. That's a nice shawl. Suddenly, the shawl seemed to come to life, standing on edge and snapping it's top corners at me as if it had just become champion boxer.
This custom, alluded to in the Talmud (Rosh Hashanah 17b), is a fulfillment of the precept of the fringed garment mentioned in the end of Numbers ch.15. It symbolizes being enveloped in prayer and in God's presence.