If the fringes are cotton and on most rugs they are,cotton is a cellulistic fibre therefore will brown on over wetting or if the ph is too high.
Clean the fringes with a m/s to remove soil and extract with hot water only,you may need to do this a couple of times to remove all soilage.Use an internal jet hand tool if you have one for better results.
Then spray with WHITE vinegar and let dry.
They will dry white.
The faster the drying the better.