The price isn't "set" from what I understand. The price is determined based on what institutional investors are willing to sign up to pay for it. So it's largely driven by the market (not on the actual stock market, just the market of interested parties pre-IPO). Those institutional investors do not want the scenario you describe any more than you or I do.

That's why it's dropping here. When the actual stock market tanked yesterday institutional investors were like - hey wait a minute this is starting to look too expensive.

Also if your 401(k) is in index funds you are safe. A company is not added to indices right away. If you are in actively managed funds or something like that you might have more exposure risk.