In certain countries they fall under quasi-bank regulations eg. "PayPal Australia Pty Ltd (PayPal) is a limited Authorised Deposit-Taking Institution (ADI) with authority to provide purchased payment facilities (PPFs)."
That gives some measure of protection on how they handle your funds, but holy shit I would not keep any money in a PayPal account for any longer than absolutely necessary. I use it as a convenient intermediary between my actual card and sellers, no more than that.