Hi there
Speaker damage can be categorised into two basic sections.
Mechanical and electrical.
Mechanical damage can be from failure of the rubber or foam suspension surround , often due to perishing from sun damage or age.
The suspension damper (aka spider) can likewise perish and get torn.
But most damage to speakers is usually electrical.
Most often this is a burnt voice coil.
A burnt coil is caused by being powered by an amplifier that has a TOO LOW power rating.
The amplifier at high volumes will produce a square wave output (essentially DC) and the coil overheats , the insulation burns off and the coil shorts out.
EDIT
''There is overload: feeding the speaker power well beyond it's rating;''
This is complete rubbish. !
Speakers do not break from overload.
I demonstrated this a number of years back to 3 unbelievers when I fed a 10W speaker with a 350W RMS (real watts , not Chinese Watts).
The amplifier was a mosfet sub amp for home use fed with a 10Hz sine wave.
As this frequency was far below what the speaker could reproduce all we could hear was the voice coil slapping the bottom of the voice coil well.
The speaker was not in an enclosure so there was no air damping at resonance.
If anything can tear a speaker apart then that would be it !..
I had that driver cone bouncing back and forth from end stop to end stop at double its normal cone excursion for 30 minutes and it was taking the amps full power --- WITH NO DAMAGE.
The reason why no damage was because the amplifier was not distorting , and also the cone was pumping cooling air around the coil.
''like tearing of the cone and speaker terminal damage.''
This is USER ABUSE , not a failure mode.
Cones do not tear by themselves and terminals do not fall off in normal use......