When the fallopian tube has burst, there is no abortion. There is removal of the ruptured and hemorrhaging tube. If there is no rupture yet, the most conservative - and most likely to preserve future fertility if the other tube is intact - is to remove the affected tube. (some doctors use methotrexate to kill the embryo in the tube or try to open the affected area and surgically remove the embryo. I believe that this is justifiable in that the embryo is the equivalent of a loaded gun pointed at the mom. But the resultant scarring increases the risk of a future tubal pregnancy, so it's better for the mom in most cases to have the more conservative surgery) The baby is usually removed along with the damaged tube, because there is no way to save him or her. The child dies because the tube dies.
This is not the intent of the procedure, however. For instance, if the docs were to discover that there is not actually a tubal pregnancy, but a burst appendix or ovarian cyst or aneurysm, they would address the actual problem and leave the baby in the uterus alone.
Unfortunately for my two friends,both had what some here called an abortion...i.e. the removal of a tube with a baby in it and one had a the exploding tube on the way to the hospital.For some sad reason,neither ever had a baby in her womb,but outside of it...TWICE.