It's a bit harder to have a record low if, you know, your company's valuation grows post-IPO.

All pop. No star.

If you could make that trade in the market then yes, you could wipe out billions of dollars. But, the market assumes that you are trying to hold as much value as possible -- you wouldn't walk around trying to sell your $10 bill for a nickel, would you?

It's a difficult question, as with any "on paper" value and what that really means. If you and I trade one share for $1, it probably doesn't affect the paper value. But if a year ago a stock was regularly trading at $30, and now it's regularly trading at $7, that does substantially change the paper value of the stock, and therefore impacts anything that depends on that paper value. What it comes down is "stock price" as a reasonable estimate of what you could sell the stock for if you wanted to. You and I exchanging a share for $1 doesn't really make it reasonable to assume $1 is now the going rate; but many shares changing hands at a lower price than they regularly did last year is a good indication that the price you could fetch for the stock today is less than it used to be.

Of course, if you don't want to sell, you could just ignore the stock price, and pretend the stock doesn't have a price even. Although even then that assumes you're not using the "paper value" of the stock in any way. For example, if you want to use the stock as payment for something (e.g. in a stock+cash transaction), or as collateral for another transaction, then its paper value matters.