The most common dryer fires probably are in the "trap," which generally is nothing more than a framed bit of window screen that slides into a slot in the dryer itself. I've been trying for years to train everyone in the household that you always check the screen every time you're ready to start the dryer - each and every load.
The flexible hose used to connect to the duct that carries exhaust air outside often leaks a bit also, so "behind the dryer" there is often a significant build up of lint. Some recommend just replacing the hose every year or so - just on principle - and of course an annual "vacuuming" behind the dryer is an oft-neglected good practice.
Most of the ducts that are installed in the wall will have at least a louvred "bird guard" or sometimes a magnetically latched "door" at the outlet, and lint may build up there, or may accumulate, especially at any bends, anywhere in the duct. Especially in the spring while it's still cool, you may occasionally find a bird nest in a duct if the guards don't work properly; and the nest is an automatic accumulator for additional and sometimes very large plugs of lint.
Lint burns (smolders) at fairly low ignition temperatures - especially if there's a good draft of air blowing over it. Ignition is most likely at the heater itself, but lint particles ignited there can lodge and start a smoldering fire anywhere there's an accumulation, when they're blown downwind in the duct.