Ive got an Infinity 1040W sub. A couple weeks ago it stopped working and I hadnt gotten a chance to pull it out of the car yet. The other night driving home it started working again. Then went back out. The amp is sending current to the woofer. Checking the volts that are hitting the sub, I am getting equal volts from the amp to the speaker posts on the sub. I checked where the wire runs from the terminal on the sub into the sub and the connections there show almost no voltage, and a closed circuit (continuity). So figuring Id hear the familiar buzz of the DMM further up stream at the terminal if it is a closed circuit I put it into the terminal and heard nada. Does this sound like a corroded terminal?
It sounds like a broken tinsel lead if I'm reading your descriptions correctly. Should be easy to re-solder if it's close to the terminal. If not, replace the woofer because it will cost too much to have it fixed.