It would happen only if they collected enough semen from the men before they all died out. Otherwise the women would die out also.
I don’t think so.
First of all, collecting enough extra X chromosomes should be easy. one ejaculation contains enough sperm for billions. But that is assuming each Xchromo sperm is only used once. they can be used infinitely via cloning. sans cloning, a thousand ejaculations should provide trillions of distinct x chromosomes.
no problem.
limiting the gene pool to one trillion sperm times one billion western women should be enough genetic variation for well over a million generations, assuming no influx of unrelated genes. we are talking plenty of time to colonize the galaxy with human westernized females.
this is where we use carl sagan’s voice and say...”billions and billions!”