I think this is what you are asking? Here is a picture of my Neofinetia hybrid. This is known as the tsuke. It is the base of the leaf where the leaf attached to the plant. As you can see I have these brown sheaves. Eventually the plant will cast it off as it continues to grow. On some of my plants, roots grow under this material and push it away from the plant.
Ryan advices caution trying to cut this material off the plant. If you somehow scratch or damage the healthy plant, you might induce infection.