Why does string-like structures form on an eraser? When you rub an eraser, string like structures form on it. How does this happen?

 A: Imagine you have a blob of stiff noodle dough between your hands, and you start rubbing your hands together, back and forth, with the blob in there.
The blob deforms under the influence of the pressure you are applying. If you squeezed your hands together without the back-and-forth rubbing, the blob would turn into a pancake- which is what happens when you prepare hand-made corn tortillas.
But by rubbing your hands together while squeezing, you are instead continuously rolling the pancake into a cylindrical shape- and you get a spindle of dough, long and slender, instead. This is what happens when you make a German noodle dumpling called spaetzle.
The eraser is a very, very stiff "dough" which is actually a bit sticky. It is in fact that stickiness which allows it to pull graphite smudges out of the surface of a piece of paper. So, when you rub it hard against a piece of paper, you are scraping off tiny bits of the rubber which then get rolled into thin spindles that adhere to themselves as you work the eraser back and forth across the paper.
