Yeah best to put your BTC and ETH on a cold wallet.
Unless they're operating a fractional reserve like a traditional bank, this can't happen. All that happens is the price of the coins everybody is selling keep going down and coinbase continues to make money from the transaction fees.
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I would think the only coins that would be at risk are the ones that are owned by Coinbase as a result of exchanges. There can't be a run on a currency exchange, they will just reject transactions once their cash distribution pool is gone. Unless, of course, they keep accepting coins with no cash or line of credit to settle. Pretty sure that would be criminal.