Brake Pedal Goes to Floor When Car is Running

I don't think the booster could make the pedal go to the floor unless there was either a bad MC piston seal or air in the lines. You should be able to do manually (engine off) whatever the booster does, maybe by pressing hard with both feet. There is a direct mechanical connection between the pedal and the MC thru the booster, if everything is assembled correctly. The vacuum just assists your movement.

The car that I had the problem with would suck the pedal to the floor as soon as you touched it.
Meaning once you touched the pedal you could take your foot off of it and watch the pedal continue on down by itself until the brakes were totally locked up.
Otherwise everything seemed normal.
I got another booster for it and the problem went away.
Same MC and everything, and I have seen it twice in 40 years so apparently it's not very common.
Both were Fords.