PayPal won't chase the debt themselves they will sell the debt to a debt recovery company. Its them who will be sending the letters.
If you look into it a bit, some of the "debt collectors" are just departments at PayPal.
Why would it do anything to your credit rating?I got scammed a few years ago and never sold a thing on ebay again. Even though paypal admitted it was a scam, they still kindly put my account into a negative four hundred pounds and refused to budge. So the debt collectors started calling and harassing and it was all pretty annoying. They sent cards telling me mr green or mr black would be calling and of course no one ever did. I never paid a penny back and nothing affected my credit rating and 6 months later all contact from the debt collectors ceased. Paypal are a joke, go let them recover the money and forget about it.