It is a fur stole.
She appears to be a fashionably dressed woman of at least moderate means. Not only the fur stole says this but also the fashionable hairstyle, the fit and fashionable cut of her clothing and the quality materials they are made of.
A fur stole would be common to a woman of moderate means.
In the re-construction era, many Black persons, no matter their position before or during the war, held positions of power and influence they were not permitted to attain before. With this power and influence comes the means to maintain the position.
The late-19th century was an era of conformity. Women of all levels attempted to get as close to the fashion ideal as possible... at least when they dressed their best. It was a mark of their family's prosperity and prospects, a credit to their husbands and his position, and a means of influencing their own peers. Black women were not immune to this if it meant that her husband and family were seen as "getting ahead" on the social ladder. Having one's photo taken, the formal portraits such as this one, was seen as a record for posterity. They took care to wear clothing and hold expressions that they felt would record them as the Person of Influence they'd like to be remembered as.
It sounds like you have an interesting family story to explore. Good luck.