In essence they are rolled into bundles of non-continuous threads and a combo of friction and being twisted together (and sometimes adhesive) holds them together.
Another example of this is to take two stacks of post it notes and interleave the pages. Now try to pull it apart. This illustrates how powerful friction is when you have something with a lot of surface area in a small volume, like in the case of a bundle of short fibers twisted together.
You can do the same thing with phone books but they aren’t as common anymore. It makes for a cool party trick.
Link for more info:
https://physics.aps.org/articles/v15/27
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