Love the idea of the thread.
So, my ideal "end of" the Joker is tied to my ideal end for Batman. For me, Batman dies relatively young. He dies saving a random family from a random mugger in crime alley, and he does it not as Batman but as Bruce Wayne. But somehow, like in a bad romance movie, the moment Batman dies, Joker knows.
And with Batman gone...Joker goes on a straight up rampage, and immediately burns half of Gotham...but there's just no fun in it anymore. Nobody can stop him, Gotham is his, and he just...gets bored, and suddenly walks off. Never to be seen again.
When Joker dies, he's an old, old man whose body gave out on him long ago and his mind halfway has, and all his many, many attempts at suicide have somehow failed (but in comedic ways, like what Joker thought was poison gas was really just mislabeled perfume), and he can't even remember what laughing is like. Since Batman died, it's been the universe that has done the laughing, and he's the butt of the joke. He dies alone, with no one to know or mourn.
To the people of Gotham, it seems that Batman and the Joker both died in a climactic battle during Joker's rampage, and urban legends about what it must have been like grow like mushrooms. No legend ever mentions Batman dying by a random, lucky bullet in a back alley, or Joker dying of old age....a sad final joke.