How do you handle entity activity outside the console window?

It just dawned on me that I only have real control over what is rendered on screen at a given time. I know that some roguelikes display the entire dungeon on the screen, so it's a less of an issue.

But what if I had a character on the screen that then walks off screen. How you go about tracking what's it is up to and it's position without seeing it?

Right now I am only dealing with what's rendered on screen for efficiency. Do I have expand that even further? What if the map is huge?