[AR2a woofer stopped working suddenly]

Could someone tell me what that wire is called?

[AR2a woofer stopped working suddenly]

I found a pair of AR2a's in the trash and with a little work got them sounding pretty good.  Recently the woofer stopped working though.  The only thing I see wrong is that the wire that attaches to the face of woofer has come undone.  Would this cause the woofer to stop working?