A US citizen who doesn't hold US passport but only US birth-cert residing in another country holding now also the passport and citizen of the residing country. If she likes to enter USA utilizing the passport of residing country and notifying the US embassy that she holds a US birth-cert, would that be okay? She prefers only when stepping to USA later to decide to get a USA passport. In that case, is she considered a USA citizen if she likes to study in a US College?

How did a US citizen get into another country without a US passport?

What country are they in now?

In general it should be OK, but they will ask why she doesn't have a proper US passport. If this person (you ?) has a US drivers license or any other ID this would be important to have on you.