Could be a protective sleeve to keep a user from putting a seat tube too close to the shock pivot. Alternative possibility is someone used a seatpost shim in the frame, accidentally lost it down the seat tube, and it's stuck by the pivot area.
"a hundred travel books isn't worth one real trip"
It is just below the shock mount, where the bottom weld is (see image below, finger point). I'm guessing it's an added tube to give more strength to the bottom bracket? I'm trying to figure out what size Fox Transfer Dropper to buy, 150mm or 125mm (external). By using Fox's calculations, I am shy by 4mm for the 150... Thanks for your help.