Fractional Reserve Banking (FRB) was practiced in ancient times.

“Roman bankers did indeed lend – much of the extensive evidence was gathered by Andreau [viz., Andreau 1987]. It can also be demonstrated, in case it needs to be, that classical banks practised fractional reserve banking – for otherwise there would have been no need in the crisis of 85 B.C. to give the bankers of Ephesus ten years to pay back their depositors. We have no evidence as to how large their reserves were normally … It has recently been asserted that ‘any interest gained on [bank] clients’ deposits had to be credited to the account of the client’, with the implication that it would have been pointless, most of the time, for them to loan such funds. But that is extremely misleading: the writer in question failed to notice that what was technically known as a depositum was only one kind of bank-deposit, generally non-interest-bearing, whereas if you wanted interest, the form of your bank-deposit would be a loan” (Harris 2006: 11; Harris 2011: 236).

Roman law appears to have allowed FRB under the mutuum contract, a real contract under which a fungible good like money was lent to a bank and ownership of the money passed to the bank. The bank was required to return an equivalent fungible good or goods in terms of quality and quantity, after a certain time or on demand. The idea that FRB was illegal at Rome or considered immoral is unsubstantiated, despite Huerta de Soto (2006).

Example of voluntary FRB:
(1) We set up our fractional reserve bank;

(2) our clients hand over money to us and explicitly agree that the ownership of their money passes to the bank;

(3) the bank gives the client a bank account, which is a credit/debt instrument or an IOU redeemable on demand to return to them money up to the amount in his or her account from (a) the bank’s reserves, (b) from sale of financial assets, or (3) loans.

(4) it is understood by all parties that most of the original money has been loaned out (except for that portion held as reserves), and only a tantundem from the bank’s reserves, money from sale of financial assets, or loans is provided;

(5) the bank’s private notes are negotiable, so that they can be used by anyone who accepts them as a means of payment/medium of exchange. It is in our contact that our clients must explain to anyone who accepts our private notes the terms as stipulated to them. The private notes are widely accepted in the community. People are happy to accept them as a means of payment, and redeem them when they wish to.

(6) if the bank becomes insolvent, the clients holding accounts or unredeemed bank notes can sue to regain their debt from the liquidation of the bank’s assets. Everyone understands this and accepts the risk.
Where is the fraud here? Risk is part of any venture.