Pretty much across the board, beged gadol and katan have fabric squares sewn on the corners.
Why do tzitzit have fabric-squares on the corners of the garment?
One must attach the tzitzis to a piece of cloth that is at least three by three agudlin (three agudlin being between 2 2/3 and 3 inches). The custom is to sew an appropriately sized piece of cloth on the corners because in many garments, even new, there are pieces of cloth sewn together that are not the correct size. Therefore, we put the correctly sized piece of cloth at the place where we attach the tzitzis. (Kitzur Shulchan Aruch 9:16)
My understanding is it's just reinforcing. Even so, over time you'll see the strings keep pulling towards the edge.
If an edge is broken, you can't just mend it: you have to take off the strings, restore the garment to its four-cornered nature, then reattach the strings.