Some minor mid information here, breakers used in residential are inverse time the larger the amount of current the faster they trip, most breakers will hold 3-5x there rated value for around 10 seconds, even fuses do this for the inquisitive type guess what the “sand” inside is doing…
What should be being asked since you mentioned old there are some brands out there that are known to be hazards federal pacific stab lock is the leader in failure to trip, lots of articles online if interested the buss is problematic and the breakers can look like new and won’t trip. Another brand is Zinsco these have aluminum busses and in some cases the buss arcs heating the breaker enough so it can’t trip , usually a fair amount of damage on the underside before failure. These are the 2 big ones yes any brand breaker can fail and conditions can make or break (pun intended) even the best brand. As Jack said the wire probably burned clear just a few strands of wire can make a really big flash but not long enough or solid enough to trip the breaker is the highest probability if other than the 2 brands above. The fact that it did arc shows there was a return path for the voltage to create the arc.