That's not necessarily true. Value is due to supply and demand. If it's not a popular or highly collected series, a coin that has a low survival might not be overly valuable.
For large cents Dr. Sheldon, auther of Penny Whimsy, did an experiment to try to calculate survival rates of coins. I forget the specific details but do remember his estimate of survival was %3 or reported mintage. He took a specific die variety of large cents were there was a very good count of the number known to exist. Keep in mind the early date large cents have been collected by die variety for over 150 years, so these counts are surprisingly accurate. So, say a certain variety of 1794 large cents is known to have 60 examples. He would go to a dealer and ask them to put together a random lot of 1000 1794 large cents, which he would attribute and take a count of each variety he found. So if he found 2 of those variety, of which there are 60 known, out of 1000 coins then he estimated for each 500 coins you would find this variety. The total population would be 500*60 or around 30,000 total pieces. Except he did the same math for all the varieties he found and calculated the total population of surviving coins based on the known rarity of each variety. While each estimate was slightly different, the estimates did give very similiar results around 30,000 surving coins. Then he took a look at the total mintage of 918,521 1794 large cent and figured that around 3% survived. He redid the same experiment with different years and pretty consistently got an estimate of survival rates of around 3% of the reported mintage. So this is the number I use to estimate survival rates. I also use this estimate, along with ebay, to do crude comparisons of the reported rarity of varieties to determine what I think the rarity is. For instance, the reported rarity of the 1845 N7 large cent is R5 meaning 35-70 coins estimated to exist. I have checked ebay twice, about two months apart, for this variety and each time I search for 1845 large cent and ebay returns ~200 coins. Each time I have looked I find 1 unattributed example of this variety. With a mintage of 4 million and a survival rate of 3% there should be around 120,000 1845 large cent. This means I should find an 1845 N7, if 75 exist, about once every 1600 coins. I find one about once every 200 coins, which leads me to believe the rarity is grossly overstated, as once every 200 coins from a population of 120,000 coins leads to around 600 1845 N7 instead of the reported 75. I am not saying there are 600 of them, but the coin in my mind is not even close to R5. Edit, I guess it's worth noting that coin loss due to melting is much less of an issue with copper then it is with silver. So the 3% survival estimate may be right for early copper and too high for silver, but the same approach to estimating the current survival rate of any coin could be done.
Early US coinage tends to have survival rates between 1.5 to 3%. By the end of the 19th century survival rates are probably running between 3 and 10%. Key dates tend to have higher survival rates than commons. So I would think between 42,000 and 140,000 probably closer to the lower end.
The online price guide I looked at showed them starting at $13 and going upward to about $1000 for a MS coin It's not only the mintage, but demand that determines value. A 1992 CAM cent just sold on eBay for 12,500 since only a single die has been discovered,
While I understand what you are trying to ask, it is a pointless question in most cases because it can never be answered. There are however some coins where an actual approximate answer can be given. That answer is known as the condition census. But in all but very few cases, the 1804 dollars is an example with 15 known, that census will be stated in a format something like - 35 to 40 known. Or 125 to 150 known. Typically the only reason that anybody would even ask the question of "how many left" is so they can try to estimate the value of the given coin. But the value of basically all coins, all but the very rarest anyway, is always pretty much known at any given time. The market establishes value. And the market establishes value based on supply and demand. But rarity alone does not establish value. There has to be demand to go with that rarity or there will be little if any value. There is a paradox. There are plenty of coins where less than 50 were ever even made. But those coins have no value to speak of because nobody wants them. And the reason nobody wants them is because there are not enough of them. Now to many people that doesn't seem to make sense. But that is the paradox. You see, for a coin to have significant value there has to be enough of them to go around. There has to be enough of them for people to collect. There has to be enough of them to make a market in that particular coin. And if there is not, then that coin will have no value to speak of. There are of course exceptions to this rule. But they are exceptions, not the rule. And that is another reason that original question is pointless. For these exceptions are very well known in the market and thus they have their own particular market where an entirely different set of rules are applied. They also have a very specific and limited market for only a very few collectors could ever even afford them. Then you have the other side of the value paradox. You have those examples of coins where a huge number of them are known to exist, but yet the coins are by any definition - expensive. Coins like the 1909-S VDB. These coins not rare by any stretch of the imagination, but yet they are very expensive even in low grades. And the reason they are expensive is because everybody wants one - demand. There is a huge supply, you can go out buy 10 of them in virtually any grade you want on virtually any day of the week, every day of the week for that matter. Again - a paradox. But that's the way the market is because that's how people are. As long as everybody else wants one, they do too. And they will pay to get it. But if nobody else wants it, they could care less. You can't give them away, even of there are only 15 known to exist. There are 15 1804 dollars known to exist, they sell for millions each. And they are not even legitimate coins. And at the same time there are other examples of coins where only 15, or less, are known to exist and they sell for bullion content. Go figure.
Here is a thread I started Jan. 09 about Morgan dollar populations and the Pittman act which melted millions of them down to be sent over-seas, while some of it became Peace dollars. Nobody knows for sure which ones took the bulk of the melting. You might find the thread interesting. It renders the mintage figures in the redbook for Morgans almost meaningless. Many people who collect Morgans probably don't even know this happened. http://www.cointalk.com/t46228/#post499026