How can a company run out of cash when its stock prices is dropping? For instance, in 2008, the Royal Bank of Scotland saw its stock price drop by ~30% in a day, and it was apparently impossible for the bank to make it till the end of the day because it would run out of cash.

Why is that so? How can its valuation affect in such a short term the cash it can disposes of?
It appears to me that it is the other way round: The RBS was running out of cash which is why the stock price was dropping. 

Stocks usually don't affect the immediate operation of a company, since they are traded on secondary markets (stock exchanges) among stock owners, not bought from / sold to the actual company which issued the stock.