The banks of Cyprus are small potatoes compared to austerity measures in Greece, Spain and Great Britain. The government on Cyprus is too small to help out with the banks so the depositors will have to come to the rescue if any financial disaster occurs. Depositors will be on the hook for any bank failings because mainstream European governments are reluctant to help the island as is remains split between two rival governments.
Both the depositors and the government should help with the Cyprus mess. I'm guessing that Greece had it's foot in Cyprus, which is why there are some problems. But I do know for a fact that there are offshore internet companies that base their credit card sales in Cyprus, so that may effect things.
I do not believe it is the depositor's responsibility to rescue Cyprus's banks. It's not their responsibility, but it sure is their problem. I personally think its best to let banks fail, while tragic it lets things equal out over time. I would advise against saving banks as America has done, its failed policy that doesn't correct the problem.
No, it is not the depositor's responsibility to rescue Cyprus' banks, because a depositor is not an owner of a bank. A person who deposits money in the bank does not receive any profit when the bank profits. Similarly, the depositor should not have to lose money when the bank loses money. A depositor does not share in decision-making for the bank, so the depositor is only a creditor, and should not lose money if the bank cannot manage itself properly.
I do not believe it is the depositor's responsibility to rescue Cyprus's banks, just as it was not the United States governments business to rescue American banks. Banks that do not function properly should be allowed to fail because history as shown that those that are rescued continue to follow a risky path.