Let's say I have the Heliod, Sun-Crowned + Spike Feeder combo in play, which allows me to gain an arbitrary amount of life at instant speed. Meanwhile, opponent has the Nexus of Fate combo running, which allows her to take arbitrarily many turns. She still needs to convert these turns to a win, though. She is playing Biogenic Ooze as her win condition, but in this case I have arbitrary amounts of life, so Biogenic Ooze is ineffective.
However ... she can continuously make more Oozes and attack for arbitrarily large damage. The board state is changing and so are our life totals, but she cannot kill me, and she cannot pass the turn and win by milling either since eventually I'll draw my Walking Ballista and kill her.
How would the game end?
Related: What happens in the event of a standoff in Magic? However, this doesn't seem like it falls into one of the standoff rules, since it's not a loop. As opponent attacks for ever-larger numbers, I have to respond by gaining ever-larger amounts of life.