Coinbase has an account on bitstamp where they hedge their net position. In times of high demand for btc, it sometimes happens that they run out of fiat on bitstamp and cannot process orders instantly.
I think that's old info, pretty sure Coinbase spreads around multiple exchanges now for their buys and sells. They haven't just used Bitstamp in quite a while.
Probably nothing. At worst Coinbase would only lose the fraction of their USD/BTC holdings that they have stored in Bitstamp, but they would continue business as usual.
Coinbase could abandon Bitstamp if they wanted to, since they have their own customers selling and buying coins (therefore providing a supply of coins, and a way to liquidate them). And Coinbase also trade coins on multiple other exchanges (according to their claims). This makes their overall Bitcoin trading activity decentralized with no single point of failure.