Whoa guys, slow down.
He's not talking about the speaker wire connection on the sub is loose, he's talking about the tinsel leads.
The tinsel leads have come loose from the solder connection where you plug the speaker wires into it? Or at the cone? I assume this is the standard tinsel layout, not woven into the spider? If its merely coming loose at one end or the other at the solder joints, yeah just resolder them. Be very careful not to drop any hot solder onto the subs suspension parts, the spider mostly as it will be directly below where you are soldering. Re-solidified metal doesn't lend itself to helping a soft and plyable material that needs to move in order to work properly.
If the tinsel wire has broken in half, you will need to replace it, not solder it back together. First off, the wire must be long enough to not pull tight as the cone moves to its excursion limits. Second, the tinsel wire must flex as the cone moves. A solder joint placed in the middle of that tinsel wire will great diminish its flexibility. Any time you have to resolder tinsel leads, it must always be done at the ends.
Lastly, whats a kenwood bandpass truck sub anyway?
Kenwood's the brand name, I got that much. But bandpass is an enclosure type, not a speaker model, and raw subwoofers really are designed for truck specifically. It sound smore like you are describing the enclosure type than you are the actual speakers. In either case, imo it sounds like an upgrade is in order.
