Anyone repair stock antenna cable?

The connector for the back of the radio pulled off the antenna cable. I cut the cable back a little hoping to find the "coax but there is just a plastic shield inside with 1 tiny strand of wire running in it. Can this be fixed or retrofitted with a more modern cable? This is for a 67 Dart with factory telescoping antenna. I'm not against using another route for an antenna.. just want the FM radio for my Sony in-dash head unit.