Pictured below is the cracked center cell of a heat exchanger from a 1989, 75,000 BTU,  Goodman
Package Unit, ground mounted on a concrete slab.

NOTICE: I'm qualified in electronics but not in HVAC. My comments and experiences may not apply to your situation at all. If you have trouble with your gas appliance, get advice from a qualified professional.
When we bought our 1870's house it had been vacant two years. There was a lot of work to be done before we could move in. When the weather cooled, I turned the gas furnace on at the thermostat and got heat. After a few days, the furnace stopped heating. I didn't know anything about gas furnaces and frankly I was, and still am, very careful (afraid) of gas.  
When the furnace quit heating, I turned the gas off at the meter and very carefully opened the
unit to see if anything didn't look right. I was shocked to find all the low voltage wires charred ...
and there was one thermal switch bypassed. I got on the Internet to find some information about that bypassed switch and charred wires. 
Fortunately, I located the Garden Web Forums. I posted my furnace condition in their Heating and Air Conditioning Forum and soon I got several responses. The bypassed switch is called a Flame Rollout Switch and the charred wires came from blower air coming through the heat exchanger compartment and blowing the burner flames back into the ignition compartment. The roll out switch is supposed to shut the furnace down in such an event and not allow the burners to ignite again until the condition is corrected. Flame rollout is usually caused by the heat exchanger being cracked. Shutdown can also be caused by the switch itself suddenly going bad. You can test the switch with an ohmmeter. If the switch tests ok, better check the heat exchanger for cracks. You might find something that looks like the picture below:
One side of the cracked heat exchanger, center cell. The crack can't be seen without removing the
top cover of this furnace. The other side, pictured below, is in similar condition.  

Instead of testing the switch and replacing it if bad, or replacing the heat exchanger if cracked, someone simply bypassed the switch and that created a hazardous situation; carbon monoxide could enter the house through that crack. I don't know what law applies but it seems to me that if  bypassing a safety feature on anything  causes death, injury, or financial loss, the person who bypassed it should be liable.

I imagine the condition had lasted for quite a while. The first air leak would have activated the flame roll out switch and as you can see, these cracks are extensive. The people who lived here before - and us - are very fortunate to be alive, in my estimation.  

The other side of the heat exchanger, center cell:
The person who bypassed the roll out switch isn't the only person who made a mistake here. I should never
have trusted that gas furnace to be in good condition without inspecting it FIRST. I'll never be that naive again! I bought a new heat exchanger, new insulation, high temp sealer, new wires, a new roll out switch and installed them myself. Then I had my work inspected by a professional. Then I fired up the furnace. IT WORKS!.  
Thanks to all the people on Garden Web Forum for help on this and other projects.