Killing a horse/donkey/mule attached to a fence while attached to a lead will not drop a lead, but it is still shown on the fence until "removed", although the lead will not drop.

When you kill a horse/donkey/mule that is attached to any kind of fence via lead, the lead will not drop, but it will still show the lead attached to the fence. When you click it to take it off the fence, it will not drop. I tested this multiple times in creative and survival with a horse, donkey, and mule, and the lead was never dropped.