The letter from HHS provides some examples, such as ectopic pregnancy, miscarriage, or pre-eclampsia. I have not yet talked to my ED or OBG staff, but I doubt if we see many such cases coming in through the ED, and miscarriage would be the most common.
https://www.hhs.gov/sites/default/files/emergency-medical-care-letter-to-health-care-providers.pdf
Even the most extreme pro-lifers that I’ve ever heard don’t call treating an ectopic pregnancy an abortion. Even though fetal death is a certain outcome. Because the primary purpose is to save the woman (and her future fertility), not to kill the baby. There have been an infinitesimal number of pregnancies outside the uterus that have resulted in live birth, but I’m unaware of any that occur in the Fallopian tube surviving to even anything close to viability. Ectopic is technically any pregnancy not in the uterus, in the tube is just the most common variant. An embryo can implant in the abdomen outside the tubes, and once in a blue moon those babies survive to be born, but it’s super high risk.
Pre-eclampsia is typically not a feature in pregnancy before 20 weeks and is often treatable for quite a while. It would a pretty rare case of pre-eclampsia that became life threatening in spite of typical treatment before the baby is viable. It’s not terribly uncommon to need to end the pregnancy before full term but this does not necessitate killing the baby. Premature birth, sure. But killing the baby is basically never an absolute necessity to treating pre-eclampsia. I’m sure there’s a case somewhere that has occurred that killing the baby was actually necessary, but that’s an extreme outlier.
A miscarriage may very well require a D&C. But that is also not an abortion (never mind the medical terminology of a miscarriage being a “spontaneous abortion”). It might involve removing the remains of the fetus, but said fetus is already dead from natural causes in that case.
I have yet to hear of a case where killing the baby as the primary goal is medically necessary, with no feasible alternative treatment.