This is a great example of a crazy quilt. These quilts date to the last quarter of the 19th century. About 1875 - 1900.
Some of the fabrics are falling apart, which is very typical of these quilts, due to the metal mordants used in the dyes. The silks are the worst for this deteriation. You will find some patches where the silk threads have gone away, leaving just the linen or cotton warp threads. This is all very normal for these crazy quilts.
Do not wash this quilt.
You can hand tack a piece of organza over the areas that are falling off the quilt to stablize those areas. Do not store it in plastic. An acid free box with acid free paper rolled up and placed in the folds is a great way to store and protect it in your home. You can buy these boxes very resonably these days from mail order houses. Be sure that you are buying acid free boxes.
Dont store on a wood shelf or in contact with wood of any kind. The acid in the wood will transfer to the textile.
If you cant obtain a box, a pillow case will also work to protect it from dust. The most damaging effects on textiles are caused by dust, humidity and light.
Crazy quilts do not stand up to hanging for long periods of time...actually none of your quilts should hang for more that a month at a time.. but crazy quilts are especially fragile. I would not hang it at all unless it is just for a day or so at a show. Even at our shows, we tend to lay crazy quilts on a table rather than hanging. I suggest just getting it out to look at it once in a while and refold in a different place each time.
When you say it is not finished, are you referring to the quilt not having a back or are there sections that are not embroidered?
Many of these quilts never had a backing applied. They cannot be quilted. I have seen some of them that have had a backing applied by seaming around the edge and tacked in a couple of places.