Assuming the inner part is still working well;
Get some heat shrink tubing from Radio Shack or the electrical supply section of a hardware store or home center. You will want something just big enough to slip over the small end. Trim back the frayed portion of the fabric.
A heat gun works best for shrinking it, but holding it over a stove burner works too, don't get it too close and keep rotating it until the tubing is tight.