Originally Posted by
DannoXYZ

That's the lug that broke.
Originally Posted by
fietsbob
It's the Plug in the end of the seat stay, that forms that logo faced piece, its a cast piece, sleeves inside a squared off end of the seat stay tube.
No, it's not the lug, and no, it's not a one piece plug. The stay ends were cut at an angle, and a flat plate stamped with the TREK name brazed over the end. Then the stays were brazed onto the sides of the seat lug.
This type of failure is usually a result of not having enough brass under the stay. When I brazed stays on I tried to fill the area beneath the stay as full as possible without spilling over onto the seat tube.
That said, an easy fix for this would be to chop the stays off flat and use a plug such as described by feitsbob: