Fractional Reserve Banking is real and is the basis of our banking system. However, it doesn't work how you've described it in the question.
This is how it works.
First depositors deposit fund to the bank.
The bank is required by law to keep a fraction of the money deposited in reserve. This is where the term fractional reserve comes from. The reserve amount varies, and I don't know what it is right now. Usually this is 10-20% I think.
So the banks can loan out up to 80% of the money they have in deposits. The reason this works is that depositors typically keep their money in the bank over long periods of time and it is rare for a bank to need to give that money back all at once.
The bank makes money on the margin of interest between what they pay depositors and what they charge people that borrow the money.
Also - via the Federal Reserve (in the US) or a national bank (common in other countries) banks can borrow and loan money to other banks. This is done at the federal reserve rate and is one way the Federal Reserve controls monetary policy. One reason banks might need to borrow money from other banks is to keep their reserve amount available.
One of the effects of reserve banking is that it is possible for the money to be loaned multiple times which seems odd, but it works.
I'll try to explain.
Let us say that in my town there is one bank - The Bank of Town.
Sally deposits $100. So if the reserve rate is 20% the bank can loan $80 of Sally's money.
Famer Joe borrows $80 from the bank to buy seed to plant. That $80 is spent at Frank's seed store.
Frank deposits that money into the bank - $80.
At this point on the banks books - they have $180 in deposits and $80 in loans.
So they can lend up to 80% of $180 - $144
So they have $64 that they can lend.
They lend $40 of it to the soda shop for a new sign.
The danger to the bank in this scenario is if Sally and Frank both decide they need their money right now and withdraw it. This is what is known as a run on the bank - large numbers of depositors pulling there money out at once. In this case the bank would have to borrow money from another bank - to cover the withdrawals until their loans get repaid.
Since the bank is still trying to make money - they typically charge more than the bank loan rate (or prime rate) in the case that this happens.
So - yes there is some danger to it. However, the bank isn't really creating money as much as it is freeing it for re-circulation.
Since the Federal Reserve system was created with the FDIC insurance program the banking system has stabilized to a large degree. The reason that banks fail now is not because of runs on the bank. The primary danger is of banks making too many bad loans. In the scenario above, if Farmer Joe and the soda shop fail to repay their loans then the bank is on the hook to the depositors for that money. A lot of analysis is done by banks on the probability of loans going bad. This is also why the credit rating system came into existence - it gives the banks a guideline for how good someone is at repaying loans.