When a multifilament rope is subjected to abrasion then the outer filaments will quickly become broken and a furry finish will develop. This furry layer will protect the yarns underneath preventing further abrasion. If this condition does not stabilise and continues to develop then there may be excessive abrasion that could lead to significant strength loss.
As the surface of a rope wears some of the filaments will break, this will result in a fluffy/fuzzy appearance. This provides a cushioning layer that protects the fibres underneath and stabilises the abrasion process.
This type of abrasion is typically caused by the environment the rope is used in and can be reduced by ensuring the rope is clean and sheaves etc are in good condition