Try this. Estimate the length of cable that's inside the frame and cut a fresh piece of housing to that length, plus enough to stick out at both ends. If there there's a a ferrule or cable stop at the derailleur end of the cable, remove them. If there's a cable stop at the head tube, detach it from the frame. Now slip the new housing over the derailleur end of the old cable and use it to gingerly push the old housing and cable out through the head tube end. When you get housing showing at both ends, remove the old cable, insert the new cable, remove the housing and trim, replace the ferrules, cable stops, and the new housing, and presto!
Also, if you do lose a cable end inside a frame tube, a J-bend spoke works best for fishing it out.