Its not common for a diagnosed ectopic pregnancy to resolve themselves once its confirmed in the tube which is the most common form of ectopic. They can suspect an ectopic pregnancy based on slow rising HCG levels or levels that rise and fall but its probably more accurate to say pregnancy of unknown location. Treatment is usually surgery or methotrexate depending on what gestation the pregnancy is at and those that do resolve themself can damage the tube (if its in the tube) increasing the chances of ectopic pregnancy again. Often if the pregnancy is of unknown location they will leave treatment whilst watching what the HCG does and scans to see if there is any change to the appearance of the tubes/ovary etc

With ectopic pregnancy bleeding usually occurs as progesterone is not high enough to stop the lining of the uterus coming away which is why alot of people still get what they think is a period or a m/c. When bleeding occurs its usually not heavy and can be described as a mucousy pink/brown or prune juice colour not the typical brighter red with clots you would expect with a complete miscarriage.

Are they suspecting ectopic based on your sisters symptoms or has a scan confirmed there is a mass in her tube? If there is a mass the chances of it resolving on its own are not as likely and I'd say the methotrexate or surgery would be the preferred method of treatment.

Rach75 is right about methotrexate increasing the risk of NTD and many Drs don't inform women correctly about when to ttc again. The good thing about methotrexate is if it works you can save the tube although if a lady has one good healthy tube her chances of conceiving again are basically the same as someone with 2 good tubes. Its when the tubes are damaged that the chances of having trouble conceiving are increased.