I have had two service calls recently that show how fires can start.
First was a Sunday afternoon call that a fused disconnect had caught on fire. I got to the home and the homeowner did have a problem. The disconnect had actually burnt all the plastic insulator material, and the homeowner had been home and put the fire out with a powder fire extinguisher, and called the fire dept. They checked the attic and declared the home safe to occupy after they turned off the 240 V breakers.
The problem was that the load lug on one leg was loose, and the bad connection caused it to heat up, and after time the connection became a resistor and eventually got so hot that it melted the insulation and caused it to burn. I replaced the disconnect with a load center with the correct breaker, after checking the furnace for a short.The bad connection never blew the fuse or tripped the breaker. This was located in a closet in his living room. He almost lost his home and maybe his life.
The second was a service call to a home where the residents went to evening church services and returned to find that the bathroom lights and some receptacles were not working. I went to the panel and found a tripped breaker and a dead short on the circuit. I found the problem in the bathroom ceiling fan. Someone had left the old fan running and it caught on fire. It had melted and dropped burning drips all over the sink and burnt holes in the rug. The only thing that stopped it was the insulation burnt on about a foot of the romex and it fused together and tripped the breaker. I learned in apprenticeship school that a fan motor bearings will start to fail slowly and create heat and eventually create so much resistance and heat that they will catch on fire without the breaker tripping. The fan was melted toast, the fan housing was burnt, the insulation on top had melted, the joist was scorched and charred , the ceiling has smoke stains, and the attic stunk. Nobody smelled the fire in the home as the attic acted as a chimney and drew the smoke up and out the vents.
These poor people could have come home to ashes instead of a house, or worse still, they could have died in their sleep.

We have to be careful and always make good connections, and I tell my customers to replace any bathroom fan that is slow, makes noise, or is old to replace it asap. Attic fans also should be replaced after a few years. Don't wait till they fail, or it may be too late.