Many localized anime games suffer from sub-par English dubbing or censored cutscenes. In the PS Vita homebrew community, a "patched" ROM often refers to an version. This restores the original Japanese voice acting while keeping the English text, providing a more authentic experience for purists.
If you already own the game and want to dump your own cartridge for personal backup, you can research (like NoNpDrm or VitaShell) on dedicated homebrew forums—but ensure you comply with local laws and only use your own legal copies.