An ectopic pregnancy does not require an abortion - it generally requires removal of the diseased part of the fallopian tube. The death of the child is an unfortunate side-affect, not the intended result.
Can't save the baby there, but the mother will die without the abortion.
Actually, the baby could be saved, but modern medical science has seen fit to focus much of its energy on new and better ways of killing unborn children instead of trying to save them. Nonetheless, there have been instances of successful reimplantation of ectopic embryos, and you will find a bit of information by googling "reimplanting ectopic pregnancy". The first hit is:
http://bmj.bmjjournals.com/talks/fraudcardiff/tsld006.htm
"August 1996: a major breakthrough - Worldwide media coverage of doctors in London reimplanting an ectopic pregnancy and a baby being born - Doctors had been trying to do this for a century. It was a huge achievement"
If the woman is unaware of this type of pregnancy (heck, some women even give birth without knowing they are pregnant!), and it goes far enough along, it does become an emergency situation.
Some women do not give birth without knowing they are pregnant. They may claim this, but it is obviously not so if you have ever been around a pregnant woman. What these women really are is in denial, and hoping that if they ignore the "problem" long enough, it will just go away.