It is already hard to dispose of old clothes once you get tired of them, once they become unfashionable or get damaged. We usually resell, donate or make them into rags. With the advent of Fast Fashion the problem of disposing used clothes even get harder.
Damaged and out of fashion clothes are even much harder to dispose because no one would wear them and more often than not they are used as rags or left sitting around taking up cabinet space.
If my discarded clothes to be used for rags have buttons I usually remove them. Buttons are notoriously hard to replace once they are lost. You usually lose only one but have to buy an entire packet which does not appeal to buyers.
There are also buttons especially old ones that command a high price because they become collectibles or are put in expensive clothes. I once had a shirt with cheap buttons where I replaced them with my old buttons but are of higher quality. People who notice told me that I have expensive clothes because of the button.
A few even commented that they would also like to replace the button from their clothes to higher quality ones to make them more expensive looking. I think this is a business opportunity for enterprising people with button sewing skills and access to high quality buttons.
I also cut out any graphics from my clothes destined to be rags especially my t-shirts with graphic designs especially if it is embroidered patches and comes from designer clothes. They can also become collectibles and put in good clothes or scrapbooks to enhance their design.
Now that the buttons and the graphics/embroidered patches have been removed you can then proceed to create handkerchiefs, bandanas, gloves and other cloth materials smaller than a t-shirt. You can also use these clothes to create clothes for dolls and pets.
What remains could be created into rags or stuffing for stuffed toys.
All these small moneymaking ideas might not be enough for you to have a meaningful income for you to live upon. Imagine however of doing this on an industrial level were you sort discarded clothes on a commercial level like buying them in bulk from garbage collectors or from companies discarding their clothing inventories.
You will then see the potential of discarded clothes for rags as a source of reliable and meaningful income.