Little resistor Thing ??
Hi Ralph, Are you talking about a defrost drain heater ?
A drain heater is technically a resistor of course and almost all early Frost Free refs used drain heaters.
FD was a very reliable FF refrigerator as were other major brands, problem is very few are lasting 50+ years or even much over 30 years.
The only real exception are GE Hot-Gas defrost systems, which also use a drain heater.
John L.