If you have had this procedure and WANT to have a baby:
One site I found said that it is possible for some women to have a tubal ligation reversed even if her tubes were cut and burned. You would have to make an appointment for a screening diagnostic laparoscopy to evaluate the tubal lengths before proceeding to reparative surgery. The longer the length of healthy tube, the better your chances are.
If you DON'T want to have a baby:
Some failures of tubal ligation allow the sperm to get up, but don't allow the fertilized egg to travel down to the uterus. In this case an ectopic pregnancy (or tubal pregnancy) may develop.