Anivia E crit for ONE damage
Playing ARAMs on my main account, I rolled Anivia and had this happen. I hit Lux with a Q stun, then followed up with an E. She had been at around 50 health but not only did she not die, her health bar didn't even move. Our Wukong spoke up almost immediately with something like "wtf? did your e not do damage?" and I said that maybe Sona healed an instant before so it just looked like no damage, but I'd check the replay.
YT:
Imgur:
https://i.imgur.com/iBlo9pj.mp4
It crit for literally one damage. You can see the crit icon and the "1" in the damage floater.