I have not seen anyone get rich by saving, but there are still many people who do, they limit their spending for themselves and their loved ones, and they think that way they will become rich. But they don't think that as long as they stop working and start spending money, no matter how much money they have, they will run out, you are right on that point.
That's a fact. When a person keeps spending their savings without earning more to save, they will definitely go bankrupt again, which is invariably not a sign of consistent wealth. Unless for old people who tend to save their wages so that when they are retired, they would have enough money to land on, and by then, they may not have lots of expenses to cover because by then, they may have had grown children who can even be supporting them in their needs. Some say money is hard to make but very easy to be spent lavishly; if one chooses a lavish life style, then it cannot be obtained by saving a whole lot of money, and one should stop saving just to lavish the already saved funds.
Savings should only be used for emergencies, other than that I don't see a second reason to save. If you want to have a rich life besides working hard and earning a high income, then investing is what you need to have.
@Smack That Ace, as an economist, savings should not only have one purpose, like you said for emergencies. It's an arguable fact, which I am in doubt of. Savings, whether for a wealthy lifestyle or not, cannot be limited to emergencies. If you work to earn a living and your salary cannot cover the cost of a car and you need to purchase one, you will definitely save to achieve that goal, or you will be deemed to take a loan and buy the car, in which case you will still need to save so you can repay the loan. There are a lot of instances to consider.