I had a team of Snapfire and Rubick who both had Blademail, but that's the only clue I found. They had random neutral items (not Phoenix egg) but they activated blademail and took 3-4 big hits at 1% HP without dying.

Supporter Benefit? Some Phoenix Egg swap-out bug?
Snapfire at 1% hp and Iron Talon-neutral should not be surviving 800 crits and another 2 hits with only blademail up. Looked like that Phoenix Egg-proc. Very scummy.