You deposit $10k in the bank

The bank originates a mortgage to someone. It uses (some of) your $10k to give cash to the customer getting the mortgage, and the customer then uses that cash to buy the house.

For whatever reason, a bank run happens, i.e. everyone comes to make a withdrawal all at once

You try to withdraw your $10,000. The problem is that everyone wants cash, not shares of houses, but the bank only has so much cash.

The bank is good for your $10k, but not on the timeframe you want it. The bank is _illiquid_, but _insolvent_.

The bank will try and sell it's mortgages to someone else for the money, but if it tries to do this all at once it will likely end up selling them at prices that are below par. In that case the bank might end up with less assets than liabilities; this makes the bank _insolvent_.

In a deposit insurance scheme, the government takes over the bank, pays out to customers, and services the loans. The government can do this because it can easily create liquidity. Generally in recent history the government still makes a profit when it reduces an illiquid bank

I agree, and IDK why it is so hard to talk clearly about finance. Here is how I understand what's been said (not an expert):

When a bank pays a loan out to its lender, it must have capital (valuable assets actually owned by the bank) to back it up. But these "assets" are not always easy or possible to liquidate, or turn into cash. This is where the other person's deposit comes it. They use the deposits for "cash" instead of liquidating the assets they own in order to pay out the loan. This is what is meant by providing liquidity.

Technically, the bank's own assets can be considered to be backing the loan, but the long-and-short of it is that YES, bank's do use the cash from their deposits to make loans, and that is why there is no money available when the bank run happens.

Disclaimer: this is my interpretation of what others on this thread are saying. I don't actually know if this is right or wrong

You deposit $100 dollars at two banks, the banks lend to each other until they have created 10x as much bank money than they have cash. The cash didn't go anywhere, it is still there but if the bank were to pay it out it would not meet its regulatory requirements and be shut down even though it might have $1000 worth of assets if you give it enough time.

The problem essentially is that the money can be withdrawn all at the same time but the obligations cannot.