Does a stock's price represent current liquidation of all shares?

"What if everyone decided to sell all the shares at a given moment, let's say when the stock is trading at $40? I imagine supply would outweigh demand and the stock would fall."

Yes this is the case. Every large "Sell" order results in price going down and every large "Buy" order results in price going up. Hence typically when large orders are being executed, they are first negotiated outside for a price and then sold at the exchange. I am not talking about Ownership change event. If a company wants a change in ownership, the buyer would be ready to pay a premium over the market price to get controlling stake.

Is the stock's price at any given moment the price at which all shares could be sold to new investors?

No. For the simple fact that the current bid/offer always have sizes associated.

What you should be looking at is the consolidated price to buy/sell X shares (10bn doesn't really work as not everyone is willing to sell/buy).

If you look at the spread of the consolidated price at your quantity level, you'd notice it would be in stark contrast to the spread of the best bid/offer but (by definition) that would be the price to buy or sell X shares to new investors.

Edit
Calculation of the consolidated price of X shares: You go through the order book and calculate the size-weighted average price until you covered X.

Example:

    bids
 1000 40.00
 1000 39.80
 1000 39.60

So the consolidated price for 3000 shares would be $39.80, the consolidated price for 2000 shares would be $39.90.

What if everyone decided to sell all the shares at a given moment, let's say when the stock is trading at $40?

It would fall to the lowest bid price, which could be $0.01 if someone had that bid in place.

Here is an example which I happened to find online:

Notice there are orders to buy at half the market price and lower... probably all the way down to pennies. If there were enough selling activity to fill all of those bids you see, then the market price would be the lowest bid on the screen. Alternatively, the bid orders could be pulled (cancelled), which would also let the price free-fall to the lowest bid even if there were few actual sellers.

Bid-stuffing is what HFT (high frequency trading) algorithms sometimes do, which some say caused the Flash Crash of May 2010. The computers "stuff" bids into the order book, making it look like there is demand in order to trigger a market reaction, then they pull the bids to make the market fall. This sort of thing happens all the time and Nanex documents it http://www.nanex.net/FlashCrash/OngoingResearch.html

Quote stuffing defined: http://www.investopedia.com/terms/q/quote-stuffing.asp

I remember the day of the Flash Crash very well. I found this video on youtube of CNBC at that time. Watch from the 5:00 min mark on the video as Jim Cramer talks about PG easily not being worth the price of the market at that time. He said "Who cares?", "Its not a real price", "$49.25 bid for 50,000 shares if I were at my hedge fund." http://www.youtube.com/watch?v=86g4_w4j3jU

You can value a stock how you want, but its only actually worth what someone will give you for it.

More examples:

Anadarko Petroleum, which as we noted in today's EOD post, lost $45 billion in market cap in 45 milliseconds (a collapse rate of $1 billion per millisecond), flash crashing from $90 all the way to an (allegedly illegal) stub quote of $0.01.

http://www.zerohedge.com/news/2013-05-17/how-last-second-flash-crash-pushed-sp-500-1667-1666

How 10,000 Contracts Crashed The Market: A Visual Deconstruction Of Last Night's E-Mini Flash Crash

http://www.zerohedge.com/news/2012-12-21/how-10000-contracts-crashed-market-visual-deconstruction-last-nights-e-mini-flash-cr

Symantec Flash-Crash Destroys Over $1.5 Billion In Less Than A Second

http://www.zerohedge.com/news/2013-04-30/symantec-flash-crash-destroys-over-15-billion-less-second

This sort of thing happens so often, I don't pay much attention anymore.

What if everyone decided to sell all the shares at a given moment, let's say when the stock is trading at $40? I imagine supply would outweigh demand and the stock would fall.

No, nothing at all would happen. If everyone decided to sell at $40, that would mean that nobody had decided to buy at $40 and there would be no trades at all. The number of shares that change hands at a given price is, necessarily, the lower of the number of shares people are willing to buy at that price and the number of shares people are willing to sell at that price.

If every current holder of the stock decided to sell at $40, as many shares would change hands as people who are willing to buy at $40 can take. For more sales to happen, people would have to be willing to sell at less than $40, which they may not be willing to do.