Unfortunately just about anything can happen. Generally credit for both stays will happen. When it doesn't I, and others, have had luck with calling in explaining the situation and the account is updated.

The funny part is many reports have come in where the longer of the two overlapping stays will not post and only the shorter (maybe because the shorter one posts first?). But it does make one think maybe they are taking the one that will cost them the least in points/nights. This drives home the point to make sure you get folios for each and every stay and keep them until after everything posts.