Doubles not infrequently came with spare firing pins in a trap pistol grip cap. The better grade of double comes with removable bushings in the standing breech, which allows firing pin replacement without disassembling the action. Presumably this was because the firing pins sometimes broke.

The Springfield 1903 was originally issued with spare parts, including a spare firing pin in a container under the trap butt plate. The removable firing pin tip on the Springfield striker was designed with broken firing pins in mind.

I have never experienced a broken firing pin with either one.

I have experienced a broken firing pin in my old pre-war Browning A-5 shotgun, which caused it to fire when the breech was closed, because the broken off tip had wedged in the firing pin hole. Not a pleasant thing to have happen, even in the hunting field.