Was writing this as Shivaware posted theirs, which also explains the situation pretty well, but including mine as I mentioned a few other things.
Negative time doesn't mean a game automatically ends, though players at the table likely have the option to kick the over time players on their turn(s). If they do this, the game will be neutralised and all players except whoever was kicked (you can only kick one or the other and that neutralises the game and prevents kicking the other) will be declared winners, and that kicked player as loser. However, this is a multiplayer elimination, one of the non-kicked players will be chosen to be eliminated as well (based on BGA account age - newer players are kicked over older ones). One of the overtime players has the newest account, so if the other out of time player is kicked, both over time players will end up eliminated, however, if the one with the newest account is kicked, a player who is not currently out of time will be eliminated along with them instead, and the other overtime player will progress to the next round.
The game has a maximum time of 2 months, so if that time is reached, the game will also end with a neutralised result - this then awards ranking based on who has most time left. So again, if things continue in that way the two overtime players will be eliminated. If another player ends up exceeding the negative time or one of those two, they could be eliminated instead. But as the game is only currently at 33 days, you're probably looking at another 4 weeks or so before it ends due to maximum time.