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When I worked in theater sound, one of the ways we used to amuse ourselves between shows was by blowing up speakers with too much sound.
No, actually there was a serious purpose. We used hi-fi speakers because they sounded much better than dedicated PA speakers, but we needed to be sure where their limits were. Fun days indeed.
One reason a speaker can blow is if you put to much power into it for too long a time.
What will happen is that the coil of the drive unit (sometimes called the voice coil) will get hotter and hotter. If that heat can't escape, eventually the coil will melt at some point and sound output will suddenly cease.
To allow a loudspeaker to go on louder for longer, designers have a few tricks up their sleeves.
One is to use wire with a rectangular rather than round cross section. That way there are no gaps in the windings. More metal can take more heat.
Another way is to fill the gap of the magnet, in which the coil is centered, with 'ferrofluid'.
Ferrofluid consists of tiny magnetic particles in a carrier fluid. The magnet of the loudspeaker will hold the fluid in place, and the particles will help conduct heat from the coil to the magnet. The magnet is large and can soak up loads of heat.
(The photo shows a blob of ferrofluid on a sheet of glass, under which is a magnet.)
But still there is a limit to how much heat the magnet can soak up, and eventually the whole thing might get so hot that the coil still melts.
So, one last trick... an external heatsink. The magnet is connected to a vaned heatsink that protrudes through the cabinet into the open air. The vanes offer a wide area through which heat can be dispersed. If you really want to go one stage further you could cool it with a fan, but I don't know of that ever being done.
However, with amplifiers getting ever more powerful, possibly fan cooling will be the next step. And after that... water-cooled loudspeakers anyone?