Create a new common treasure for the loot tables called "Certificate of Participation" and make it a guaranteed loot drop if you go 0-4.
The problem with this is it would encourage people to enter league matches and just quit right from the start to get that extra chest.
I think when @LieutenantCommanderData said going 0-4, he means playing and losing all 4 games. Also, I understood his suggestion as just funny idea to mock those who loses all matches because the treasure is only of common rarity which doesn't really increase the gold gain all that much.
In germany theres the term "golden pineapple" for a forgettable or irrelevant outcome. Would make a nice treasure. Maybe bump it to uncommon. Golden Rasperry might have more international flavour, no pun intended.