I'm not an expert.
but I drive a few cars (buick,chevy,ford,dodge )
and they all stop.
I'm not sure about all models but the ones I've worked on .
" Yes " it does just sit there ,the pedal holds it in , the rubber boot holds some "when new" but it's just a dust cover .
Sounds to me you need to do some adjusting /longer rod/a stop on the pedal / something (quote > to keep my brake pedal from falling forward and pulling out the rod) . hope that helps.

T L