Bianchigirl beat me to it for the caveat regarding some Dia Compe aero levers. These used a hemispherical ferrule for a cable housing stop in the back of the lever. If you're not precise in pushing the cable end through the hole, you can dislodge the ferrule and it drops into the lever. And thus unwrapping the tape and body removal follows. @$#$^@#$.

Congrats on your success. Next time, if you're pushing the cable through unlined housing (which sounds like what happened), dab the end with a little crazy glue. Keeps the strands tight while negotiating tight bends.