It is not going to close.
Feel free to come back here quote me and kick me if I’m wrong, but the show is still running on London, on the road, and multiple international tours. It’s made more money than God or the Angel Moroni and they’re not going to let the Broadway production close overnight because of an insurance accident. (Let alone on the eve of what was to be The biggest celebration of the show since its opening.)
There’s no way to guess what the extent of the damage is at this point- for all we know it will be back up and running by Labor Day, or even sooner. But even if they can’t get it back by the holidays, between insurance, money made from other productions, and yes, if need be, a small temporary infusion from the creators, they can ride this out. (To say “they don’t need it” when talking about Stone and Parker is technically true but tone-deaf – the creators of South Park can easily afford a negligible investment to ensure it doesn’t close like this.)
In fact even in the worst case scenario I can easily imagine a timeline where the show reopens a year from now, with the 15th-anniversary celebration reconstituted in some way (with an asterisk next to the “15”), and because of the circumstances and savvy marketing and audiences being ready to see it again, it suddenly becomes one of the hottest tickets in town again for a year or two, which alone would make the reopening worthwhile.
Hopefully it doesn’t take half that long however. (And yes my hearts go out to the current cast and crew, likely to be the ones most affected by this for the near future.)