The same way you do it with computers: avoid central control.
Central control is fragile, non scaleable (and promotes corruption when human beings are involved).
More importantly, it is possible that most people are wrong on some particular question about a market. If so, a sudden discovery of the truth by the mainstream might lead to a desertion of this market.
Self-fulfilling rumours which trigger bank runs can be a distributed phenomena
If we were to get rid of the physical token of our monetary value, it would be impossible for a run in one bank to negatively effect all of them. After all, an electronic 'withdrawal' has to go somewhere.