Xenon bulbs are very different to filament lamps. Xenon is gas discharge I think and are the more expensive bulbs vs cheaper filament lamps.
HIDs work off a ballast which provides a massive voltage (at a fairly low current) to the lamp to excite the gas and produce a photon discharge a bit like a neon light I think. This is different to the filament lamp which basically has a high resistance bit of wire in the bulb which glows when you stick 12v through it.
This mean you've got two possible causes of your problem - the ballast may have failed and therefore failing to ignite the bulb, or the bulb itself has died.
HID bulbs last a very long time, something like 40,000 hours or more, which equates to about 5 years constant use, so should last longer than a normal filament lamp.
Be very careful when you're changing the bulbs in these things, you shouldn't let any oils from your skin come into contact with the bulb as you'll knacker it. Also never ever turn the lights on without a bulb connected, if you turn the lights on and therefore activate one of the ballast units without a bulb connected you risk frying the ballast.
1999 156 1.8TS Sport Pack 3
2001 166 3.0 V6 24V Super
2003 156 GTA 3.2 V6 24V
2005 156 1.9 JTDM-Jet Sport
2008 159 1.9 JTDM Lusso
1997 GTV 2.0TS Lusso
2001 147 1.6TS Lusso