From all my days where I was destructing speakers on purpose, I've learned a lot by finding out the hard way.
Any speaker that has had any melting of the glues that are used internally (this is caused by heat over the life of the speaker/glue), the speaker will not function the same anymore. Much like your car wheels go out of alignment, this can happen to a speaker. Speakers are under tremendous stress to produce low notes.
Usually, these alignment issues are not so significant if they happen on the cone, but when it happens to the spider or the voice coil the speaker will now be twisting itself little by little as it moves back and forth. This causes a farting or rattling noise at xmax, or a catastrophic failure at/near the xlim of the driver.
Basically, you should re-cone this speaker. The kit is cheaper than the driver.
EDIT: Taking a look at the pictures, it appears that the glue that has held the spider onto the frame has come loose. This is Xlim damage. there might be some other problems happening that caused it, but your problem is caused by the failure of the spider.