you may achieve it using curve hair from blender 3.3

Here is what I quickly made:

Here is the node set up. I colorize the importants node, the orange one is where you will choose which object the curve hairs base should be shrink wrapped to. Tweaking the value of the green node on the left will allows you to increase the distance between the fibers of the rope. Tweaking the gradient on the green colorRamp node will allows you to choose precisely how close the fiber are (left of the ramp is the base of the fiber and right of the ramp is the tip of the fiber / white color means not close, black color means so close they touch each other)

Here is where I get the knowledge about the new 3.3 hair tool: https://www.youtube.com/watch?v=NF49gQcqIy4&ab_channel=THELUWIZART

Here is the official blender file to train with this new tool: https://studio.blender.org/films/heist/gallery/?asset=6072

you may achieve it using curve hair from blender 3.3

Here is what I quickly made: I order to have the same result you will have to use EEVEE as the render engine and set the curve shape to stip in the render properties. increasing the "additional subdivision" value will smooth the strips

Here is the node set up. I colorize the importants node, the orange one is where you will choose which object the curve hairs base should be shrink wrapped to. Tweaking the value of the green node on the left will allows you to increase the distance between the fibers of the rope. Tweaking the gradient on the green colorRamp node will allows you to choose precisely how close the fiber are (left of the ramp is the base of the fiber and right of the ramp is the tip of the fiber / white color means not close, black color means so close they touch each other)

Here is where I get the knowledge about the new 3.3 hair tool: https://www.youtube.com/watch?v=NF49gQcqIy4&ab_channel=THELUWIZART

Here is the official blender file to train with this new tool: https://studio.blender.org/films/heist/gallery/?asset=6072