All the countries I've lived in during my life (4) have had various types of "boxes" on the street where you can dump clothes, which subsequently gets donated to various organizations that handles giving clothes to people in need. Since I've found this in every country I've lived, I thought this was ubiquitous in the modern world. Am I maybe blinded by my experience here?
In my country, those boxes go to discount stores operated by these charities which really aren't that cheap. A lot gets discarded, I've heard, because it's not presentable for purchasing. It's a bit sad, hopefully yours are better.
Of course there are negative effects as well, like the eventual dumping of items on poor countries and the effects on domestic markets for clothing in those places... but at the scale the West buys and discards clothes, there's really no perfect answers.