"여자아이가 개를 잃어버렸어요."
Translation:The girl lost her dog.
Adding -버리다 to a verb imparts a feeling of discomfort or relief. This sentence expresses the former.
And this one expresses the latter: 다 끝내버렸어요 (have finished everything at last).
There's no possessive "의" used in this sentence so I think both those answers should be accepted as well.