The Xbox (now known as the original Xbox) was released by Microsoft in 2001/2002. It stands out as it's Microsoft's first foray into the console gaming market.
Due to that emulating the Xbox is harder than people thought, there isn't much progression in emulation or preserving the console. People thought that because it was a PC that it was easy to emulate but turned out to mistaken with most early Xbox emulators or translators abandoned after getting their first game working with problems. The major hundle in Xbox emulation is the custom Nvidia graphics card that was used and there is little documentation about it. Made matters worse that a recent discovery that some games used LTCG to optimize the code making them harder to detect without full scale emulation. Don't expect much more progress any time soon.
There are only two active emulators for the console both at an early state and hard to recommend at the moment, they are Cxbx Reloaded and XQEMU. Cxbx Reloaded runs a few games in particularly Jet Set Radio Future with sound however a lot of games don't work. XQEMU is more accurate than Cxbx Reloaded and can run Halo however it is a virtual machine that is very complex to set up due to focused on developers rather than users, requiring a special file that is very hard to dump, knowing command line, slow to run the games and no sound. Again like Cxbx Reloaded many games don't work however it does have better compatibility if you know how to use it.
MAME also emulates the Chihiro arcade system that was based off the Xbox, just with extra memory. There is progress made on OutRun 2 however it is extremely slow on powerful computers, no sound, no inputs and some graphical glitches.