Paypal policy does not allow them to go into the bank account. At least in US,  probably that violates some of fed laws or something. In case of negative balance they keep calling your cell and landphone if they have it on file, send paper mails to your billing address and try to freak you out with dozen of other ways. They even send a report to all three agencies (Equifax, Experian, and Transunion) in order to demolish your credit score. Still they never go to your bank account by themselves, you've to authorize each and every transaction.

The problem may only arise if you have a subscription active - they'll charge a subscription's full amount from your CC/BA, take out what's theirs and send only a remainder piece to the requesting merchant. Most probably such action will result to your subscription being cancelled by the merchant due to 'unpaid' event and whatever service you're subscribed on you'll loose access to.