How do you think that would work? Whatever you mean by "end of a civilization", it's going to have nearly zero effect on polygamy. Polygamy is a marriage practice that people will do, or not do, according to their culture; changes of government / technology / etc. don't change it.
Going back up to my original example, you see polygamy practiced in China in the warring states period (ca. 500 - 200 BC), in the early Han (ca. 200 BC - 0), and the later Han (ca. 0 - 200 AD), and the three kingdoms period (ca. 200 - 300), and the Tang dynasty (ca. 600 - 900), and the Song dynasty (960 - 1279), and the Yuan dynasty (1271-1368; wasn't even a Chinese government), and the Ming dynasty (ca. 1368-1644), and the Qing dynasty (1644-1912; also not a Chinese government. The Qing actually outlawed foot binding, though this was not effective.), as well as through all the other intermediate periods not mentioned in that list.
However you want to count the end of a civilization, there won't be any relationship at all to polygamy practice; one changes and the other doesn't.