On the blower housing is a control thermostat and a fuse. Both go to the burner in series. If either is open then no power will get to the gas assembly but the dryer will still run.
Both the flame sensor and flame ignitor are wired in series with each other. If either one is open nothing will happen. The flame sensor will open with the heat from the ignitor and when the ignitor shuts down then the amp draw is then applied to those coils, they open the gas and whoosh! Houston we have ignition.