They can suspend your account, take you to collections, and put a negative report on your credit score. At least in the US, other countries may be different.
A quick google search reveals lots more, and none that I saw saying companies can’t come after you for a disputed charge. Most won’t, and most of those that do will only do it if they can clearly show they’re in the right, and you should be able to beat any collection attempt if they aren’t, but they can try.
Prime example: gym memberships