The reputation of the bank actually doesnt matter anyway because once the entire economic system of a country fell apart, no matter how great their previous reputation is then they will probably fell apart too. A bank is not a standalone company because it relly on the country's economic system as well
But that is not that sudden when we are going to make some safe deposit and the economic fell. That is not too coincidence. I think bank reputation is the first one people think to make safe deposit
The chance for that to happen is pretty much close to zero indeed however you should take into account that that safe deposits are meant for atleast 1 year which means that there is a whole year for that to happen. There are also several factors that will trigger the potential of the fall of the economic state and it will takes several years and alot of "warning" before that potential threat to happen however it is not impossible for it to happen at the faster rate.
Also that this has nothing to do with the bank's reputation or whatsoever because what matters will be the economic state of the country. As I have stated previously that no matter how great a bank hold its reputation or how good they are in providing liquidity, once the economic state fell then it will fell as well