Chromosomes don't stay intact like (it sounds like) jonsen is assuming. Instead they cross-over or re-combine to make never-before-seen strands -- the new strand has one end from one copy & the other end from the other copy.

There are maybe 2-3 cross-over events per chromosome per generation in humans, e.g. https://biology.stackexchange.com/questions/19005/how-many-r... .