빠져나오다 and 빠져나가다.
It is the difference between 오다(come) and 가다(go).
It is similar to English. 오다 is when the result brings smth/smn nearer to the speaker, 가다 otherwise.
ex)
회의 중인데 빠져나왔어.
=> I slipped out from a meeting. (the speaker is now "with" the listener, so 빠져나오다)
용의자는 경찰의 포위를 빠져나갔다.
=> The suspect slipped out of the siege of the police. (the suspect is now somewhere away from the speaker)