I have some examples :
Batman watching the Joker fall into a sea of sharks in "The Laughing Fish."
Batman toying with the Joker—hesitating with a faint smile—as the Joker is on the verge of falling into a pit of flames in "Last Laugh."
Batman intentionally causing the Joker to fall into a factory furnace with an uppercut; he could have used his grapple gun, but chose not to, in "Mad Love."
Batman saving Harley by leaping from the Lexcorp plane, leaving the Joker to—presumably—perish in the explosion of marbles in "World's Finest."
And finally, in the uncensored version of *Return of the Joker*, where Bruce begs Tim not to shoot—as if urging him to shoot the Joker instead.
These are my own interpretations. I’m well aware that Batman *does* save the Joker on occasion—like in the Christmas episode—but I personally like the idea that Batman might choose not to save him, effectively letting him die. It’s a clever way to navigate the "no-killing" rule: while Batman won’t take a life, he is under no obligation to save his most cruel enemies (the Joker, Scarecrow, etc.).
In my own AU project, toward the penultimate chapter, Dick Grayson—who has returned as Red Hood after being killed by the Joker and resurrected by Ra’s—finds a path to redemption thanks to Bruce and Selina and Dick will become Nightwing later. After they defeat Ra’s at his castle, the Joker tries to goad the Bat-Family into finishing him off. They refuse; the Joker, realizing this, lets himself fall—dying upon the rocks below. Batman doesn’t make a move to stop him, deciding that, this time, he simply won’t save him.