If an animal is put on a leash that is held by a player and not by a fence, the lead will completely disappear after logging out of the world and logging back in. It doesn't break and drop, it doesn't become invisible and it doesn't glitch out, it simply disappears totally like it was never existed.
- Put an entity on a lead in a singleplayer world
- Leave the world
- Open the world again
→ The lead completely disappears