Since the voltage drop across all the filaments in series may be less than the full 117 volts from house's line voltage, it is necessary to get rid of the excess voltage. Usually it is an ordinary power resistor getting rid of the excess voltage. Find a replacement with the same resistance and power ratings. Higher power ratings can be used for more reliability.
Power resistor is a good replacement for the hard to find line-cord resistor.
The third wire is a resistance element to get rid of the excess voltage. Since a line-cord resistor is used in series with filaments, if it is broken the radio's tubes will not light up. In some situations it might be possible to fix the broken line resistance. When it is not possible, a power resistor can be used to replace the damaged line-cord resistor. The following steps will help you to find out the specifications needed to replace a line-cord resistor for a power resistor.