From Human Action, Chapter 17, Section 12
"But now, we assume further, one bank alone embarks upon an additional issue of fiduciary media while the other banks do not follow suit. The clients of the expanding bank - whether its old clients or new ones acquired on account of the expansion - receive additional credits, they expand their business activities, they appear on the market with an additional demand for goods and services, they bid up prices….In order to settle the payments due to non-clients, the clients must first exchange the money-substitutes issued by their own - viz., the expanding bank-against money. The expanding bank must redeem its banknotes and pay out its deposits….The instant approaches in which the bank will - after the exhaustion of its money reserve - no longer be in a position to redeem the money substitutes still current. In order to avoid insolvency it must as soon as possible return to a policy of strengthening its money reserve. It must abandon its expansionist methods."
Mises makes a powerful statement here. Leave banks free to compete. Accept that one or more banks might issue excess credit. Understand that, as market participants recognize this they will demand instant redemption. This will force the issuing bank to either reduce the excess or quickly go out of business before doing much damage.
Mises does not make any statement advocating the outlaw of fractional reserve banking, at least not in this section. He is quite clear that it is the market that will best regulate expanding banks, and that clients of the expanding bank and especially clients of its more conservative competitors will be vigilant regarding the bank's risky practices.
This is just as one would expect an advocate of free markets to consider the situation. Mises does not condemn fractional reserve banking to the point of utilizing government force to control it. Elsewhere in this section he describes how government intervention inherently results in complacency on the part of market participants, what today we refer to as moral hazard.
"But even if the 100 per cent reserve plan were to be adopted on the basis of the unadulterated gold standard, it would not entirely remove the drawbacks inherent in every kind of government interference with banking. What is needed to prevent any further credit expansion is to place the banking business under the general rules of commercial and civil laws compelling every individual and firm to fulfill all obligations in full compliance with the terms of the contract."
Here, Mises is quite clear that even a 100% reserve standard, if backed by the government, does not remove the risks of government interference in banking. Treat banks as you treat every other business, under general laws, and the market will regulate the banking industry in a much more effective manner than would the government.
"But, some people may ask, what about a cartel of the commercial banks? Could not the banks collude for the sake of a boundless expansion of their issuance of fiduciary media? The objection is preposterous. As long as the public is not, by government interference, deprived of the right of withdrawing its deposits, no bank can risk its own good will by collusion with banks whose good will is not so high as its own."
Mises is clear that a banks good name is everything - there is no such thing as a cushion of reserves that will protect the bank once its good name is questioned. In this light, he rightly states that a bank wouldn't voluntary join hands with banks other than those of unquestioned integrity. It takes years to develop goodwill, and minutes to destroy it. Without a good reputation, a bank in a free-market environment would not last long in the market - a significant barrier to purposely risky behavior.