To be quite frank, that white fibrous string thingy looks like the Common Peroneal nerve which runs from the outside of you ankle, along the outside of you knee area all the way up your leg, via several branches, to your Sciatic Nerve, and into your lower back as the "cauda equina" or "horses tail". Thats where your spinal cord goes from a solid cord structure in your thoracic spine to a bunch of smaller branches in your lumbar spine which resembled a horses tail to those Latin speaking folks who first discovered it waaaaaaay back in the day. Yay anatomy classes of so many moons ago.
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It may very well be a clot, but the location, color, construction, length indicate its possibly nerve tissue. Blood clots are like jello when you hold them when they're relatively fresh. If still alive, the assorted clotting factors solidify them, and eventually break them down when the body senses the clot is no longer needed. I've held large clots of human blood before. Very interesting sensation and texture.