What happened in 99 is already factored into the market. The public stock market is dying to short sell over hyped companies that under deliver.
The situation right now is unprecedented. With the Fed keeping interest rates low for so long. LP's have no other choice but to invest more of their money into public stock market and the private markets through VCs. I can't seem reduce their exposure until there are viable options. The Fed won't let that happen.
I can see a scenario where if somehow startups burn up all their capital and go under. Somehow the entire VC fund goes under. LPs might have to pull money from public equities to cover their startup investment losses.
If one or two big startups like Airbnb or Dropbox go under. The worst case scenario could be really bad, as it could have sever ripple effects through the start up ecosystem. Eventually hitting the public markets and normal people.