Time Travel (or System Clock Manipulation) has been an exploitable flaw in many games throughout the years. I can recall using it in Pokémon Diamond/Pearl to import from my GBA files more quickly. People use it to access events long passed in their Animal Crossing files today.
There are fail-safe systems to avoid abuse, anti- soft-reset systems were used in the Mystery Dungeon games for the GBA/DS (red and blue rescue teams) and I believe there was also one used on the Gamecube Animal Crossing although I have no personal experience with it.
One particularly interesting case is an anti-time-travel trap wrapped around a time-gated system which misleads players about how it actually works within Paper Mario 1000 Year Door: