Think of a git repo with all of the miners maintaining the master branch. If suddenly a majority of miners wants to create a new branch and they are over 51% of the miners, the new branch becomes the master branch.

Both branches still work. All coins before the fork apply to both branches, however, after the fork,both branches are different, any new coins purchased apply to only one branch.

It's essentially two coins at that point. Then essentially it's up to the payment processers like coinbase to decide which one to support.