Burned up conductors on electric furnaces are a common problem as they age. Furnaces, Heat Pumps and AC units need to be serviced annually. The manufacturer's warranty usually requires this.
This is from Trane but most manufacturers have the same requirement:
ELIGIBILITY REQUIREMENTS: The following items are required in order for the Products to be covered under this limited warranty:
•The Products must be in the same location where they were originally installed.
•The Products must be properly installed, operated, and maintained by a licensed HVACservice provider in accordance with the Product specifications or installation,
operation, and maintenance instructions provided by Company with each Product. Failure to conform to such specifications and/or instructions shall void this limited
warranty. Company may request written documentation showing the proper preventative maintenance.
•All Product parts replaced by Company under this limited warranty must be given to the servicing provider for return to Company.
•Air handlers, air conditioners, heat pumps, cased or uncased coils and stand-alone furnaces must be part of an Air Conditioning, Heating, and Refrigeration Institute
rated and matched system or a specification in a Company provided bulletin or otherwise approved in writing by a Company authorized representative.