Sharp have quoted 60k hours backlight life. I don't know of any such statement from other mfgs.
Some sets have it user-replaceable. Some require an engineer (officially). Either way, provided they are still made/available, it should be a cheap and easy job - it doesn't, for example, need any setting up afterwards.
As for 'how' they go - I'm guessing suddenly as with a fluorescent tube. Brightness may drop slightly in use, but not to any visible extent, I think.