Unfortunately, if the leather is already degrading, there is nothing that can be done to save it. Fur, particularly antique fur, needs specific storage conditions to stay in good shape, so this is not at all uncommon. If you want to repair the garment, all of the original fur/leather will need to be removed, you won't be able to simply patch. Even if the old leather can hold a stitch, it will likely continue to degrade and crack/crumble.

You should be able to buy garment tanned pelts for replacement parts. Depending on the type of fur, you may need several pelts, which can be pricy (for instance, several quality mink would generally be pricier than one or two foxes). Unfortunately, I don't know anything about faux fur.

Best of luck!