I was playing an aram with elise and was going after a kennen and rappelled to stop taking damage I went up at 60% health came down at around 20% health. I'm not sure what was attacking me to do that much damage while I was rappelled but I almost died while Invulnerable.
Rappel makes Elise untargetable, but it doesn't make her invulnerable to damage. Any DoT effects that were placed on you before you went untargetable will still damage you while in this state. Going untargetable does not break tethers either, such as Fiddlesticks' Drain, Swain's Q, or Karma's W. Any tethers placed on you beforehand will stay on you and continue to damage you as well.
Now, I can't say for sure if this is a bug or not as I wasn't in the game, but if the enemy team had any DoT or tether abilities, then that is likely what damaged you while in Rappel.
