I had a few situations in which I apply Bleed, Burn, etc. (damage-over-time effects) on enemies, and I was able to drop them to their "Panic" state during their battle (during my turn). However, whenever I got all enemies to their panic states and the battle switches over to the "What enemies do you want to kill?" screen, the bleed, burn, etc. triggers once more before I make a decision, and the enemy just kills themselves before I'm able to decide what their fate is. After the battle, the game treats it as they were kill, and still gives me status cards, etc., which I don't want since they died outside my control (hence, the bleed trigger).
Do a battle in which you apply bleed or burn on an enemy, knock out enough HP in which they go to their panic state, and do this when they have some bleed left after going into their panic state. The bleed will still trigger after going into the panic state. Try to do this during the player turn, though, and with only 1 enemy in battle.