That's correct. They've issued and sold shares to put cash in...

That's correct.

They've issued and sold shares to put cash in their own accounts... i.e. investing in cash.

They borrow money at wholesale rates and then lend it out to punters at retail rates. As long as asset prices are stable and customers pay their mortgages on time everything is hunky dory and it's all easy profits and the more customers want to borrow they more they borrow from the local wholesaler with the only condition being that they hold a fraction of the loan book as cash on hand just in case things one or two customers go belly up. The trouble though is that when when the cycle reverses and wholesale interest rates go up they increase the retail rates to their customers which makes it harder for punters to repay the principal while at the same time property values get pushed down... so if it happens on a large enough scale they'll have a huge number of customer defaults that exceed the fraction of the loan book that they were required to keep as cash on hand.