Shadow banks are just non-banks. They include insurance companies, brokers and dealers, pension plans, money market funds, and finance companies.
The banks are not intermediaries for savers. This is a myth. Banks do not lend out depositor money. But non-banks are intermediaries. When you buy a whole life insurance policy you are putting your savings to work financing construction projects. When you lend your money to CIT, you are financing accounts receivables of some corporation.
The money in banks just sits there doing nothing. It is inert. And there is about $10 trillion of money in banks not in checking accounts (where it is doing work). Non-banks activate savings.
Since the great recession non-banks have become the bad guys and recipients of restrictive legislation and regulation. And, low interest rates which is a sin, have reduced the economic activity of many non-banks. Which reduces the velocity of money.
There are a lot of savers who, because of the sin of low interest rates, have reduced their spending which has reduced money velocity. There would be seniors and others very happy to put some of their savings into non-banks and earn some interest income and in doing so not only put their savings to work but also spend some money they normally wouldn’t.