I work in a shop and many frames with internal routing come with plastic tubing in place like this:



That tubing will terminate at the outlet and stick out like it does here. Usually, it's taped to the bike frame so it won't retract into the tubing.

As a result of building bikes which arrive like this, we save the plastic tubing for when we have to re-cable bikes with internal routing. Simply slip the tubing over the existing cables before yanking them out. It's a good idea to tape them to the frame on one end or another. Pull the cable and you're left with the plastic tubing in place, ready to accept the new cable. Once the new cable is installed in the run, remove the tubing from the free end.

If you yanked your cables out before doing this... do what others have suggested.