How old is the well? If the well is older, is there any trees or landscaping around it? I have seen this exact scenario of the well not kicking off and the fibers that looked very similar to those you have shown in the pic turned out to be root/wood fibers from how they grew into the line going down the well. I was 100% betting against the fibers being wood but I was soon proven to be wrong. Perhaps not your case but your situation is so close to what I experienced I wanted to ask. The tree that resulted in a massive about of work for me was a mimosa tree about 15' away from the well. The line going from the house to/down the well was old black pipe I believe the plumbers said was polyethylene? Anyways, with age that stuff became horribly fragile and the tree grew roots right into it resulting in fibers very similar to your pic.
When I pulled the top off the well (concrete lined well dug in late 50's) the pump was running and water was spraying right at ground level and simply falling back into well. I thought I had a easy fix but I was wrong!
When I pulled the top off the well (concrete lined well dug in late 50's) the pump was running and water was spraying right at ground level and simply falling back into well. I thought I had a easy fix but I was wrong!