The preservation of software is deeply tethered to hardware accessibility. Because original Xbox 360 consoles suffer from hardware failures like the infamous Red Ring of Death (RROD), software emulators are necessary to keep these games playable.
Keep in mind that some games may require additional setup or configuration to play, and not all games may be available due to licensing restrictions. However, the Internet Archive provides detailed instructions and support to help you get started.
archive.org/details/xbox360iso (Change the URL filter to "Uploaded by: Xbox360ISO" for the best results).