So, I think I know what happened. The short story is that they gained more than 2,147,483,647 life (aka they caused a 32-bit integer overflow).
So, they have two [[Phyrexian Vindicators]] on the field. If damage is dealt to one, they can target the other. If one has lifelink from something like [[Basalisk Collar]], they can just keep targeting each other to gain life. With [[City on Fire]], the vindicators do triple the damage to each other, so the damage quickly goes up exponentially (x^3). That means they gain life exponentially, eventually stopping it by targeting something else like you or another creature. In this case, they kept going until they had over 2 billion life, which would only take 18 damage swaps.
Did they take a turn doing something like that? If so, they were BMing you real bad lol.