Fimbriectomy is a very uncommon type of tubal ligation that is performed by removing the end (fimbria) of the fallopian tube leaving only the tubal segment attached to the uterus. After fimbriectomy, if the remaining tubal segment is long enough, the end of the tube can be opened and 'new' fimbria can be created by a procedure called a neofimbrioplasty. These "new" fimbria are not actually fimbria, but they are the cilia from the inside of the fallopian tube that have been exposed by everting the tubal lumen much like the petals of a rose are exposed once the rose blooms. These 'new' fimbria are much less effective at collecting (catching) an egg that has been released from the ovary than the real fimbria that had been removed during the fimbriectomy performed by the surgeon who did the original tubal ligation. During a neofimbrioplasty the tubal end is opened and folded back (marsupialized) so that the tubal end remains open and exposing the internal lining of the tube.
