It's very different from a bank, primarily because consumers/payers don't deposit anything, they keep their bitcoins on their device.
Only merchants, who want to receive extremely cheap Bitcoin payments -- the fees are set by the market, but a thousandth of a cent is completely reasonable -- can choose to trust one or more issuers. They may redeem/"cash in" the payments they've received at any time; the more often they do this the less the risk but the higher the fees, but they choose their own risk profile. And if the worst comes to the worst, merchants lose a week/month of income (if they choose to redeem every week/month), the issuers dies, and the merchants will probably survive (assuming the lost income is not fatal to their business). So the bad issuers are flushed very quickly, and merchants can adjust their risk/fee ratio as they desire.