A rope base lamp will not fray as long they are looked after properly. Made with coiled rope and constructed securely, each lamp design has been crafted to stay in place, and most models thermally seal the rope ends or use adhesives to prevent fraying.
If you do encounter some fraying, there are ways to prevent it from continuing to unravel. One easy DIY way is to lift the fraying end of the rope and hold it away from you, then, using a lighter or a match, hold the rope around 5”-6” above the flame. Next, lower the rope down until the fibers begin to melt and seal themselves. This method only works for ropes made from synthetic fibers.
For natural fibers, wrap the frayed end tightly with twine. Then, gather the frayed ends and apply a spray adhesive to keep the fibers together.