If timing chain breaks,will the car get fire?

I am quite not sure what you mean by "fire"! But having said that if you are referring to the electrical impulse that provides the electrical spark for the spark plugs, The timing chain or belt has nothing to do with that. The timing chain/belt turns the cam shafts that opens and closes the valves @ the proper time so the engine can fire under compression or push out the exhaust and pull in fresh air for firing again.

If the timing chain breaks, the engine will stop immediatly, but there is no risk of fire. The main problem with this situation is that, if one of the valves fluctuate, it might impact with the cylinder head and make a big problem, a costly one. You'd have to open the engine to look at the cylinder head to see if it suffered any kind of damage. My suggestion is that you replace the timing chain before something like this happens and you get a bigger headache.