Yupp, usually not all legs are connected, the same package can be used for the ones that use the extras legs, the ones that are not connected are then used for stability and support, and the ones that use more then one lining are transformers and they use them, if the big top would break off it would still work, it's just unmagnetic ferrite.
The only way for it to stop working is if one of linings burn off or the varnish on the linings gets so hot it melts and burn.