As an initial note, I have not seen any plausible claims that a crypto crash would cause liquidity problems for the financial system. As a reult, I would need to guess to the mechanism.
I do not think “liquidity” is what anyone should worry about right now. For a firm we need to distinguish between illiquid and insolvent.
- Illiquid: the firm does not have enough short-term assets (“cash”) to meet short-term liabilities.
- Insovent: the net worth (equity) of the firm drops below zero.
A bank loan is an illiquid asset. As a result, loan losses do not directly cause illiquidity; they cause insolvency. Of course, people will not normally lend short-term to an insolvent bank, so it will be illiquid later. (If the concern is about money creation, impaired deposit growth would only be a consequence of insolvency.)
Can a crypto crash cause a general wave of insolvencies? That is difficult to answer, but we can look at the possibilities.
The credit risk at the time of writing appears to from individual investors borrowing to buy cryptocurrencies. The only business borrowing that I am aware of is by the crypto exchanges - they borrow to support customer borrowering. Such loans are covered by two parties - the customer, and the exchange. We cannot double-count these debts as a result.
As for customers, banks either lend against collateral, or cash flow.
No sensible bank would lend against most crypto-currency collateral: most of the cryptocurrencies are designed so that authorities cannot seize them. Unless there is an exchange-traded fund (which can be used for margin debt), such crypto-based lending will be negligible.
Banks could lend against other collateral, such as a second mortgage. However, such loans are backed by both the home as well as household cash flow. People take out second mortgages to go on vacation or to fund small businesses (which mainly fail); there is always a safety margin for the banks in such lending.
Unsecured lending is lending against income. The recent wave of banks blocking cryptocurrency purchases via credit cards is a sign that some are getting uncomfortable with such risks. However, losses would only materialise if the involved investors are cash-flow impaired (lose their job in most cases). Although such cases will happen, any losses need to be looked at in the context of other sources of loss, such as those caused by medical emergencies in the United States.
In order for these losses to pose a systemic risk, it would probably require large job losses, which by itself poses a risk.