Paypal has fought very hard not to be classed as a bank (which comes with regulations and certifications).

As far as I know, paypal doesn't do fractional reserve banking (because it's not a bank and that would be illegal), it just collects a fee on the seller's side for each transaction, so everyone pulling out all of their money at once would probably not be that disastrous, supposedly they do have that money just sitting in an account. It would be disastrous to paypal as a business, and they would probably use fine print to keep that money, but out of greed, not out of lack of liquidity.

Their European branch, PayPal Luxemburg, has a European banking license. The US company maintains that they are not a bank. So it kind of depends on where you are, or which arm of PayPal we are talking about.

I don't think they do any fractional reserve banking though (at least they didn't two decades ago), so there shouldn't be any liquidity risk. All dollars in deposits should be backed by real dollars.

Why would they have liquidity Crisis? Are you picturing Paypal customers holding in Paypal considerable Balances? 99% of the customers use it only as an Intermediary. Money goes in : Money-Fee goes out. Unless they are doing scetchy things in the meantime there is no risk of liquidity here. Maybe I'm mistaken and nowdays People are keeping huge Balances in Paypal but that has not been the case in the past afaik.