When you get close to the survivor NPC, you will hear a ding sound and the goal (e.g. Prison Break) will pop up. You will also see a small white dot where the survivor is located, and as you get closer this turns into an upside down triangle. Approach the survivor and scroll to ‘rescue’ them, at which time you can choose which delving to send them to. If you don’t have a delving yet, the survivor will stay there until you can establish a delving.

You can find these survivors in campaign or sandbox, whether you've completed the world or not. Let's get searching!

Campaign: Orc Town in the Mines of Moria, inside a prison cell
Sandbox: Orc Town on the First Level, may not be inside a prison cell so look around
Video demo:
In the big room just after you get to the bottom of the Crystal Descent||, will be bare-knuckle brawling some wolves
Campaign: Lower Deeps
Sandbox: Cavern Deeps in the Second Deep
Video demo:
On a lower level hiding in a corner
Campaign: Upper Halls in Dwarrowdelf
Sandbox: Upper Halls on the Third Level at 157 fathoms deep
Video demo:
Will be just before the entrance, this survivor will look dead but rub some stone on it and you can revive them!
Campaign: Gundabad Encampment, which is the orc encampment in Desolation
Sandbox: Gundabad Encampment in the Third Level at 156 fathoms
Video demo: