It is a hugely interesting question which is at the heart of the current crisis. The strangest bit is that all banks require to borrow huge amounts inter-bank - how can a market be created if everyone wants to borrow - and of course part of the answer is that there are other participants apart from banks in the inter-bank market.
The more fundamental part is - if inter-bank participants do not lend to banks, what do they do with surplus funds - answer: they place it with the Central banks - at a rate below inter-bank. Is it not possible that the Central Banks could act as a broker to recirculate those funds into the market at a much greater rate than they do now?
When this current crisis is eventually over, there will be a return to good old-fashioned banking values whereby a bank is largely funded by its own depositors. This will severely limit their capability to expand rapidly - or to boost the economy. Capital will have to be rationed and directed towards productive sectors. We are looking at a massive reduction in residential construction (which eats up capital for long periods) for quite a long time