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This makes twisted rag-yarn which looks to be quite sturdy and strong, and can be made as long as you want. All you need are strips of scrap fabric, and scissors (and something to wind the twine onto). And lots of time, true, but it looks like the kind of thing one could do with half one's attention. This doesn't need two people to do the twisting. It doesn't need special methods of cutting in order to get the longest strips possible; indeed, if the strips are longer than your arms it would probably make it a bit awkward working with them. (The method looks similar to what I do to put my hair into a two-strand braid (though the twine needs more twisting).)

This method makes a rug with fewer holes since the t-shirt yarn is used as a core to crochet over, rather than being used to crochet with. One would need sturdy yarn to do the crocheting with.

This is a nice clear tutorial for how to get a continuous strip of t-shirt yarn from the main body of a t-shirt. It takes advantage of the fact that one is working with a tube of cloth, so this method will work for things like pillow-cases, stockings, trousers, and socks too.

Rather than just making strips and sewing them together, make a spiral. This would also work for things other than sheets (though sheets would give the most yarn more efficiently) Then this yarn can be used for making (knit, crochet) rag-rugs.