If I remember correctly, tubes do not stop working unless they are cracked/broken or somehow lose their vacuum. But the burnt band you described is going to cause diminished performance, thus your lowered, but not total, loss of sound.
I'm not 100 percent sure if I'm right, its been a while since I've messed around with tubes. But I hope I helped anyway,
Andrew
Synesthesia Studios
I'm not 100 percent sure if I'm right, its been a while since I've messed around with tubes. But I hope I helped anyway,
Andrew
Synesthesia Studios