https://www.paypal.com/us/webapps/mpp/paypal-safety-and-security Is their information.

Now, if someone accessed her bank account and that bank account was linked up to the paypal, then I can see how that info can all be taken. However, any big corporations, no matter their security measures, can be 'hacked' into. Target was one of the recent companies whose personal info was taken for Credit cards and more. You always sign up for email notifications on paypal and your bank, and I think that there may be texting alerts as well for when you make a purchase and such. I always log in a few times a week (if not once a day) to make sure everything is good. I won't say it can't ever happen, but the chances are usually low.

I wouldn't hesitate to call Paypal and see if they have extra security features if it helps your mom feel more convinced. OR let her know that Paypal is being used in physical shopping centers now. If it wasn't that secure companies wouldn't chance it. If something ever happens to your paypal account (not your bank account), ALWAYS call paypal ASAP. They usually fix these things for you.