I have heard some goodwills and other thrifts will save old blankets, towels and other linens for animal shelters, which is a great gesture. And other stores will send the unadoptable clothes to outlets (there is one in Phoenix, for example), where people can buy the clothes or fabric very cheaply by the pound.
The last step some charities do is bushel up what fabric materials are left and ship them overseas. For some countries, this is a major industry. And it seems better than having children scour dumps and landfills for whatever rags they can scrounge.
Basically, I would like to see usable things continue to be usable until the very end. At my house, all unwearable clothes (stuff after donatable items are donated) get stacked up for possible sewing supplied or placed directly on the ground in my yard as a bottom layer of mulch.