They’re typically copper caps or rings(sometimes aluminum), situated on(or around) the magnet’s pole piece/gap. Variously: called flux stabilization, demodulation or shorting rings. ie: http://www.audioheritage.org/images/projectmay/technology/1500AL_draw.gif and: https://celestion.com/speakerworld/patech/4/117/Demodulation_Rings/ This has a page, with a nice diagram: https://www.focal.com/sites/www.focal.fr/files/shared/catalog/document/Sopra_WhitePaper.pdf
Why not underhung voice coil?
Most of the speakers have overhung voice coil, meaning that magnetic gap is very narrow and most of the coil sticks out. In underhung design magnetic gap is (horizontally) wide and whole coil movement is contained within the gap. It requires much larger magnet, but supposed to be more linear (lower distortions), especially for big excursions. It applies mostly to woofers, but there are even tweeters with underhung coil. Very few speaker companies use underhung design. One of them is Acoustic Zen. As I understand it the only disadvantage is increased cost because of much larger magnet, but it should be irrelevant, at least for high end/cost speakers. Why overhung coil design dominates. Please help me understand.