Leech Burns are supposed be inflicted when a Leech gnaws at you when at 0 SHP or when wounds are converted by the Leeches. However I got some from a leech I acquired during foraging. Not being able to dismiss the chance that I simply had some wound that was converted, I decided to try again and incurred 22 Leech burns while having plenty of SHP and only Beesting wounds. They didn't go away. From what I can gather, one of two options is in play:
Leeches have chance to give Leech Burns even when you have SHP to spare. If this is intentional, it can be punishing to players with less resources and MHP and even cause them to die.
Leeches "try" to heal Beestings but fail, yet still inflict the Leech Burns.
How to recreate: Equip Leeches. IF that doesn't work, equip leeches when Beesting wounds are present.