Translation:In the end of the evening, nobody can leave the house.
http://french.about.com/od/grammar/a/negation_double.htm The ne ... plus in this sentence should give the idea of 'no longer' or 'not anymore;' this sentence needs tweaking.
It looks like quitter takes an object -- "I am leaving you" -- "Je te quitte" -- while partir is leaving in the general geographic sense, without an object -- "I left at four" -- "J'ai parti à seize heures"
Interestingly enough, "pas" itself is a word that didn't use to be used in the general negative construction, but became grammaticized later. For constructions that modify the negative construction (ne ... plus, ne ... person, ne ... jamais, etc), "pas" is still omitted.