[morzh]

In fact what you see in the center, the rigid piece of paper through which the screw goes, is actually the spider. Does not add to quality sound, but that is how it is.

I guess you could try to unsolder the voice coil, remove the screws holding the cone and then this central screw, remove the cone (never done it myself but I think this is how it should work looking at the speaker) and try to clean whatever crud or some other cr.... which is in there, and then replace the cone and center it.