If this is possible, I really want to understand it.
As far as I understand it, the only thing that should have happened is rear brake failure, dangerous, but no front brake failure.
Some electronic controls may have some complexity I am unaware of.
Overheating brake fluid or pads can cause softness or failure.
It's hard for an emergency brake to do this, especially if it wasn't on hard enough to prevent driving.
It won't affect the front brakes.
Emergency brakes usually are mechanical, so have no effect on brake fluid.
The crudest emergency brakes use a mechanical cable to tension the standard rear brakes, drum or disc.
Superior units have a separate caliper or totally separate brake set on the rear wheels, typically drum brakes on a disc rear system.
The hydraulic system is normally two systems in an X pattern.
Both must fail to lose braking.
Better systems use three.
Without some other failure you should not have lost braking.
I think your son is right.
I would really like to know more.
If this can happen, I need to know how it is possible.
I'm glad you survived this.
Can you describe how the pedal behaved at the time?