Speakers don't go bad, they get blown up. If that happens on full power with a tube amp you could damage the tubes or OPT or both because of excess voltage and arcing and the like. Tube amps don't like to be run without load. Semiconductor amps don't care.
I agree that you need to always have a load on a tube amp and that (almost all) SS amps don't care. For tube amps that load gets reflected back to the output tube via the output/impedance matching transformer (the result of which is a high impedance load to the output tube) and keeps the output tube from drawing too much current and dumping heat into the primary of the output transformer. Kinda like flooring a car in neutral - not a good idea. Don't even turn it on without a load. It might not get damaged the first time, but why test fate?
Lotsa ways speakers can go bad without being blown up, but being blown up is a leading candidate.
- Lead wires can get disconnected between the terminals and the VC. This can happen for a number of reasons including metal fatigue, manufacturers defect, over-current, over-extension and corrosion. There is probably a few other reasons. I've managed to save a couple of speakers by reconnecting the leads between the terminals and VC. In fact voice coils can fail randomly - mostly due to manufacturers defects or age/corrosion/material failure.
- Of course there are mechanical failures that can occur that hurt the speaker, but don't open-circuit the VC. Those can be: VC bottoming that deform or damage the VC, spider sag, surround sag, surround failure (foam rot, etc.), magnet shift, corrosion, manufacturers defects, kids with fingers, cats with claws, Pete Townshend, etc.
I hope this is helpful.