Sat, I didn't really follow what you were describing, but if surgery is done on a speaker and the connection is made inside at a point that leads only to the woofer, then only the woofer will operate. If it's made inside at a point where both the woofer and tweeter follow in the crossover, then obviously nothing has been changed from the outside terminal connection and both will continue to operate normally.

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Enjoy the music, not the equipment.