Only the state is immune from bankruptcy

In a fiat economy, an organisation which has deposit insurance is not a bank in the conventional sense, it is part of the government. Only the state (not banks) is immune from bankruptcy. If an organisation is able to be insolvent and go out of business (as all free-market institutions are) then it is able to describe itself as a bank, otherwise it is part of the state.

It is incorrect to describe an entity which cannot go out of business as a bank.