When quitting to title while a furnace is on, the furnace will continue burning after you log back in, but will not use up its burn. Other effects can occur, but I'm not sure entirely what these are. They appear to just be losing items and such.

To replicate: Place a few cookable items in the furnace, I used 3 raw porkchops. Then place a fuel, I used 1 charcoal. After 1 porkchop has cooked and the 2nd one is halfway through cooking, exit to the main menu. When you load up your save immediately after this, the furnace will retain its fuel animation without indicating how much fuel it has left.