I actually have Endometriosis and I get cyst ALL the time. I'm almost 11wks and I have a 8cm cyst on my right ovary now. If it's a true cyst and it's not hard and filled with only fluid then YES it does dissolve on it's own. She probably gets them every month and they will usually dissolve when she gets her monthly cycle, but of course now that she's pregnant it probably wont dissolve as quickly. If it's just a cyst then it wont harm her baby. I think people get cyst and fibroids confused. A fibroid will not just disappear and is something that will 9 times out of 10 grow as rapidly as the fetus does, and will more than likely need surgery to be removed if it gets too large and starts to interfere with other regions of the body. I'm pretty sure her OB isn't worried about the cyst b/c again it probably wont effect her pregnancy at all.
i had my third u/s done today qwith this pregnancy, i am 8 weeks 4 days and i have a cyst of 3 cm, i spoke to the sonographer and she confirmed what i have read on this site before, that a cyst in early pregnancy is perfectly normaland it even helps the pregnancy to progress, i have had a cyst with my lasdt two babies and they have caused no complications, I hope all goes well for your cousin.
cysts on the ovarys dont just disapear unfortunatly my friend suffers from them but on the plus side she has had children the doctors will just keep an eye on the cyst to make sure the pregnancy is ok tell your cousin to try not to worry so much i know it can be scary i was with my friend all the way through her pregnancy and i know what it was like for her so good luck and best wishes