devtrackers.gg
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.
That sounds likely. I'm not positive how edge cases like this are handled currently, but in at least several years ago the rules backend was using effectively unlimited-sized numbers, but the client was using 32-bit signed integers for things like life, power, toughness, etc.
As long as you're talking about values between negative two billion and positive two billion, there's no real difference. But outside of those ranges you can get weird display issues like this