In some rare cases it is a possibility.
Tubal sterilization procedures can fail -- either very soon after the treatment or as long as 10 years afterward. Failure rates, the reason for failure, and the timing of a failure all depend on the type of sterilization procedure and the skill of the surgeon performing the procedure.
Tubal ligation is often performed at the time of a cesarean section or immediately after delivery. The procedure, often called a Pomeroy tubal ligation, involves lifting the tube in the mid-portion, creating a loop. A slip-knot or noose-like knot is slipped over this loop of tube, and the knot is tied. Then a segment about half an inch long is removed from the tied-off portion of the tube. During the healing process, the two tubal ends are still held together until the suture (stitch) dissolves, which occurs in two to six weeks, depending on the type of suture chosen. Once the suture dissolves, the two cut ends separate. However, suture breakdown may be delayed due to some unknown reason, enabling these two ends to grow together again where the segments have been cut and tied. The result is a functional tube.
Many women say that they have had a tubal "ligation," but they may have had other types of sterilization procedures such as an electrosurgical tubal coagulation procedure ("burning") or laparoscopic placement of elastic bands or clips across the tube. Electrosurgical procedures depend on burning a sufficient length of the fallopian tube as well as complete scarring as the tubal damage heals. If you resume sexual activity too early after this type of surgery, the tube may not yet have scarred shut. Later failures may result from formation of a fistula (opening) that could allow the sperm to escape into the pelvic cavity and reach the egg.
Another theory is that sometimes a small area of endometriosis forms at the site of the cut, forming a hollow track between the blocked ends of the tube that somehow serves to connect the ends.
In all of these cases, there is a greatly increased risk that the pregnancy will implant in the fallopian tube, at the site of the healed sterilization procedure. One likely reason for this is that a new passageway might be wide enough to enable tiny sperm to pass through (moving toward the ovary) but not large enough to permit the larger egg to pass (moving toward the uterus). The fertilized egg thus cannot pass beyond the site of the surgery. Pregnancies that begin to grow in a place other than the uterus constitute a serious complication called ectopic pregnancy.
Luckily, pregnancy rates after sterilization procedures are quite low. But if pregnancy is diagnosed after a sterilization failure, an early ultrasound must be performed to determine the location of the pregnancy. Early detection is key to avoiding the serious and often life-threatening complications that may occur with ectopic pregnancy