What happens when the resistance gets too high? First, there is power lost in the wire and the speaker will not play as loud. More important, as the resistance in series with the speaker increases, it makes the amplifier look more like a current source. This means the speaker frequency response will tend to follow the rise and fall of its impedance curve.
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As the wire resistance increases, it becomes significant compared to the speaker impedance. It will affect the areas of lower impedance values first and eventually will be audible. Speakers with small impedance variations versus frequency, and that don't dip below the nominal impedance, will be more tolerant of higher resistance in the speaker wire. On the other hand, speakers with large variations in impedance that dip below the nominal value will be much easier to notice. If the speaker has constant impedance versus frequency, the only change will be reduced output.