Eh, it's not too bad don't worry. If you don't pay and there isn't a valid card or bank account linked then they'll just blacklist your details so you'll essentially be banned from Paypal.
If they decide though that it's significant enough to get the money out of you and you put in legitimate information they'll set debt collectors onto you to try to get the money back. But that's practically a worst case scenario, unless it was thousands they probably wouldn't care enough to get debt collectors on you.
EDIT: Ooops re-read the OP, okay so it's thousands still doesn't mean it's definite that you'll get debt collectors but if you do best option would be to pay it off since it'll probably tarnish your credit score, etc and generally cause a bunch of problems.
On the bright side if you don't get debt collectors then you'll probably be mostly fine aside from a lifetime ban from using Paypal unless you sort it out.