When the pets auto pickup items or deaths breath they go to the owner of the pet and not the person they were assigned to when it dropped when playing local co-op.
So if player 1s pet picks up a pile of deaths breaths they get all of them, and players 2-4 don’t get any, despite some of them being allocated to players 2-4.
Or if player 2s pet picks up an item for player 3 player 2 gets the materials.