Quote from DontMissTheBus:
First, you said "If there is less incentive to lend then could it cause a bank run?" But let's ignore that the fact that you weren't talking the deposit side for a second get to the meat of your argument here.
No. If you are talking about individual bank runs, then you are positing the scenario that some bank gets so hard by withdraws that it greats its own run. This is idiotic for two reasons. First: the shift in savings vs custodial deposits is likely to be reasonably well distributed across all the banks in the economy. Second, the whole point of the FDIC system is to prevent this from happening: in addition to reserve requirements, the FDIC alleviates the fear of bank runs in any individual bank because it stands by to guarantee the deposits. Since there's no systematic withdraw of capital, it cannot become a systemic problem to endanger the whole FDIC system.
Finally, your point about international outflows is legitimate - except a free floating exchange rate regime balances it out by making it more expensive to move assets out. Obviously, there are vast complications. But is it really worth talking about a scenario that requires movements of capitals so large as a (%) of the target investment? Far more things will complicate that kind of movements than what we are talking about here.