Usually the dream in which is seen the umbilical cord, shows the shortage of personality. Maybe you are afraid to stay on your own, where all of the responsibilities depend on you. When the dreamer cuts the umbilical cord, then it shows the need of getting on your own. Prepare yourself for the hard work, otherwise you will be dependent on others forever.
Dream dictionary: Umbilical cord dream meanings
If you dream of seeing yourself being attached with the umbilical cord, then such dream indicates your desire to be protected by others. Perhaps you do not feel good while being by yourself.