West Elm Sweater Wool Rug. Rugs by type area rugs. Shedding of loose fibers may occur but will diminish over time. This is what the west elm website says about the shedding:

If style is high on your list, west elm's charm wool rug won't disappoint. Only used for about a year. If you ever have a wool rug that feels brittle, or breaks easily, that is a bad sign.
Gallery of West Elm Sweater Wool Rug
There is no direct sunlight on the rug. $598 at serena & lily. Either it was bad quality wool to begin with, or it has been so heavily chemically processed, that it has become weak. If you ever have a wool rug that feels brittle, or breaks easily, that is a bad sign.