A semi possibility
Semi conductive, that is.
This thread (pun intneded) has me scratching my head, but I do have some possibilities.
The first is that you have some unusual form of Litz conductor. Most of these can be rendered solderable by dipping them in a solder pot - an iron might do it, but usually not. There are a few Litz-like conductors out there that do not respond (very well, if at all) to a solder pot and those need to have the microscopic thin layer of insulation removed by abrasion, such as one of these machines:
http://www.eraser.com/catalog.cgi?mode=details&product_id=1391
However, by your description you might well have a metallized filament (like an inside-out Litz) or some sort of semi-conductive filament. Neither of these would be solderable by heat AFAIK, but would instead have to be terminated by crimping or using a conductive adhesive. In any of these cases the termination process is likely very precise and very specific to the "wire".
Kind regards,
Ray