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If no one can transfer bitcoin out of the PayPal system then the only way for you to sell it for $47,000 is to find someone else on PayPal willing to buy it for that amount (or actually a bit more because of the spread). So PayPal don't lose anything.

Admittedly this doesn't sound right to me, but it's what the parent commenters seem to be saying.

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It doesn't work like this. If paypal's customers decide to cash out as a whole, then that means there is a net sell. There won't be enough buyers in paypal to cover the sells. They would need to expose themselves to another market by buying / selling actual bitcoin to be able to float like you describe.

In most financial systems, there has to be a "banker" to make the market, i.e. they have to close the deals when the aggregate buy/sell deals end in surplus or deficits. So Paypal has to close the ending position -- at least that is my understanding.

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