You're actually more likely to see 1% then any other health amount. At 100%, any damage reduces you to 99%, so we can extrapolate that down the line, if you're exactly at 50% health, and take 1 hp dmg, you'll be at 49%. This breaks down at 1% though, because you can't go to 0% because you're under 1% hp.1% actually encompasses 1.99% down to .01%.
The one and only champ who does this **** confirmed is Hela. no matter whether you have a 100 neurotoxins or buff immuntiy or fate seal or concussion she'll dealt on 1% for half a second before dying