This is a deep one. As linked by one for the books over on Metafilter, a GitHub user with the username MrWint was looking at the code of the Olympics-like DOS minigame collection “The Games: Winter Edition.” They wondered why it seemed to be impossible to achieve better than a certain score in some of the events. It turns out to be because of failed copy protection checks in most of the versions of the game produced after the initial release. Most of the cracks of that game that can be found on the internet are affected. They even affect two later official physical releases, and GOG’s release, which is a terrible problem for people who bought any of those versions expecting a working game.

Here’s their description of the result of the checks, and here’s their lengthy writeup of the problem, what causes it, what it does, which versions don’t fail the check, and a fix for it. Both pages have animations of the bug in action. Here’s their patcher.
Here’s a tl;dr summary, although the most interesting part of it all is the reverse engineering and description of the problem. But in case you aren’t interested in that and just want the gist:
The original release came with a code wheel copy protection system, and performed a number of checks for the event that the protection was bypassed. A value was created as the result of the check, and was modified and stored in various other places. Each of the events itself checked one of those places against a second, obfuscated copy of the code wheel’s lookup table. If the original wheel check is bypassed, which happens for most of the versions of The Games: Winter Edition now, illegal or legal, those places won’t have the correct value, and the game will sabotage those events during play in different ways.
It’s really sneaky, and as it turns out, it also affects the GOG release of its sequel, The Games: Summer Edition in a similar manner, although cracks of that game managed to fix the sabotaged events.