You can replace it. It is possible, though unlikely that there is any writing on the part that would tell you the value of it. It looks like it has been VERY hot. From reading, the actual speaker has a VERY low impedance (less than an ohm). The resistor is to prevent overloading amps. I would say a 4 to 8 ohm 10 watt resistor (whatever you can find) would be OK.
I see you also posted to AVS forum. Their answer was the same as mine.