Hi, welcome to Just answer! My name is Ross and i will help with your question.This material that's coming out of your exhaust will be a type of fiberglass, this is what is used to absorb the sound and silence the exhaust. Often the internals can disintegrate allowing the fiberglass to come loose. Ideally the back box will need to be replaced as it can block the exhaust, however if you pull the loose fibers out its should be perfectly safe to use in the short term. It will need a new back box to cure the problem, its not overly expensive but you do have a choice of fitting a genuine Peugeot exhaust back box or an aftermarket, I'm not sure how much the genuine parts are however aftermarket are usually under £60 for the back section, some models had a single system fitted which either needs to be cut to join the new box or a whole system fitted which is a bit more expensive so its best to take it to a garage for a quote. It usually takes about half an hour to replace or an hour if the system needs to be cut and joined.
I hope this answers your question, If you need further assistance with this please feel free to reply, otherwise if your happy with my answer, please remember to rate me! Thanks, Ross.