WTF....never heard of this.  Is there any substantiating documentation from any manufacturer pertaining to this?  I couldnt find any.  The rubber surround is plenty flexible, as it should be.  The "spider" aka...the fiber mesh below the cone that keeps the small end of the cone/voice coil symmetrically aligned with the pole piece/magnet section is supposed to be stiff as long as possible, preventing the voice coil to contact the pole and magnet.  The voice coil should keep its resistance/impedance consistantly throughout its life (or until severe heat has taken place).  As far as the cone breaking in, the cone should be as rigid as possible as well, preventing distortion.  Wimpy cones do warp under large power especially in a sealed box, causing bad distortion.  What possibly needs broken in?  My research does not uphold this break in theory.

For the equipped members: Check this out: Set up a speaker(sub)/amp/signal-tone generator, and an adjustable strobe.  Use a bright crayon and mark the cone 5 times starting at the inner part of the cone going out creating a star-like marking.  Set the Generator to a low input signal and crank it!!!  Initiate the strobe and adjust the frequency to match the sub.  Ive done this in lab tests and you should see the "High Quality" crap I've seen!!!!

For the un-equipped members:  Even when specified subs are installed in the correct sealed enlcosure, the cone is stressed, sometimes warped due to chamber pressure and general weakness.  This is visible becuase the marks show up in the same spot every time the movement of the cone and the flash of the strobe coincide.  But, the marks are very wavy when looked at an angle.

Sorry, I work in a laboratory with alot of time to spare.  Have fun and crank it!

I doubt any of the speakers/subs blew in the above cases because they weren't broken in. It definitely sounds like a user error (IE: didn't take the time to set the gain correctly, cranked the bass boost, a leaky/mis tuned sub box, etc.).

Well, after boring myself with internet research on this, Im only giving in half way because we got reputable big guy over here, and reputable big guy over there, one saying yes / other saying no.  For some its a belief, others its....something.  Even this Dick Pierce stated "I always wondered what is being broken-in the speakers or the listener's ears?" along with other lengthy explainations.  So, I am going to be good enough to admit, since "Physics" was mentioned, that everything in such case is involved.  This gives me another project to introduce to the lab in two weeks, so i can see for myself being that I dont believe in magic or phenomena, just the facts.  I still havent been able to find a manufacturer that implements this into any documentation.  Does anyone have a lead?

Have fun, keep it cranked!

Here's a procedure I learned that is fairly simple to use to break in a woofer.  If you are installing your own woofers, be it for car or home use, and have found this thread because you're the type who wants to go about the installation systematically, covering all bases, then this procedure is for you:

You need a test tone CD  (here is a download) with a 10 minute track of the tone that corresponds with the Fs of the woofer.  You need to be able to hang the woofer up in mid air, through one of the mounting holes in the frame, letting it hang freely.  There should be no walls close to the woofer, and the woofer certainly shouldn't be laying on the table on its magnet (as you often see in videos).  The nearby table or wall acts to compress the air behind the cone so avoid those types of disturbances.

The idea is to play the sine wave tone through the woofer at resonant frequency in free air.  A very slight amount of power will enable the woofer to move at full excursion.  You have to first find out what the Xmax is so that you can look at the excursion and gauge (by eye) the approximate excursion you're putting the woofer through.  A subwoofer with a one-way excursion of 12 mm would look like its moving about an inch as the voice coil moves back and forth.  You'll note that you are allowing only a few watts of power to reach full Xmax, so be careful with the volume control.

If you're working with a car subwoofer, you can prop the trunk lid and hang it from that.  If you're working with a home sub, you can hang it from the ceiling of the room near the amplifier.  Play the tone at Fs, watch the cone movement while adjusting volume, and let it flap and whirrr for the 10 minute period.  It will sound more like a fan than a subwoofer.  Allow 10 minutes cooling time, then run it again a few sets.  Your woofer is now broken in.

There is only a small percentage of DIYers who will go through this procedure.  They are the ones who make sure they have a test tone CD for setting gains, who make sure they damped all the sheet metal while the car is torn apart, who made sure they grinded all the paint off the metal before securing the ground wire.  This is just another of the steps to ensuring that when you are ready to debut the system, it will sound the way you had hoped it would.

Kicker? Cool, Ill check it guys!  I put in my lab order today for a sample, the equipment is already set up.  Im gonna put myself to the test....uh, as well as the speaker.