Most women with ectopic pregnancies do not need surgery.

http://www.patient.co.uk/health/ectopic-pregnancy-leaflet

In summary

• Ectopic pregnancy is common. The pregnancy never survives.
• The typical first symptom is pain in the lower tummy (abdomen) after a recent missed period.
• As the pregnancy grows it may tear (rupture) the Fallopian tube, requiring emergency surgery.
• Planned treatment before rupture occurs is best.
• Most women with ectopic pregnancies do not need surgery