The first example that comes to mind are peat fires smouldering through the centuries-even heavy rain won't put them out. The lowland areas of Indonesia has peat that has accumulated for 7,000 or more years. If the peat is exposed, it dries quickly and then can ignite easily. Once burning sometimes the fire goes deep into the earth and is almost impossible to put out. Fog and rain come and go and the fire burns on.
Fog is a cloud near the ground.
You need fuel and oxygen to make a fire. You can certainly get the fuel so getting sufficient oxygen to the fuel is the first question. When it's foggy, water vapor in the air condenses out to form tiny liquid water droplets that remain suspended in the air. When water vapor condenses, it does reduce the oxygen in the air but not by much . Dry air contains about 20 percent oxygen.