I work for a financial institution processing software company, so I can give you an exact answer on this topic as per the USA.
Assuming the system is ONLINE and able to provide a response within a 1500ms (1.5 second) latency period, the institution is able to specify whether or not a request for a deposit/withdrawal is accepted. However, if the system is offline or unable to provide a response within that latency period, the network goes into "stand-in" mode. Each Financial Institution sets its own limits for stand-in mode that are recorded by other machines that make up the network. If the system decides to use stand-in mode, it determines based on your activity so-far today whether or not you're in excess of the limits your FI has set. Usually these limits are (relatively) high to prevent people from getting screwed over in stand-in mode, but it means that theoretically if you knew when a system was going down you could overdraw your account up to the daily limit and the system would just have to accept that later and bring your account balance negative.
