There are a lot of variable involved. Cheaper cartridges use synthetic diamonds that don't last nearly as long as premium styli that are carefully cut and mounted so that the crystal structure is oriented properly to minimize wear.
How the user handles records and cartridges will also matter. If records and styli are kept clean, they last longer. According to one manufacturer (Benz or VdH, styli can last as long as 2,500 hours if the records are kept clean). I've used Lyra cartridges for close to 2,000 hours with no problems or sign of deterioration in tracking ability.
The rubber suspension parts of cartridges can go bad from aging and exposure to environmental agents (primarily ozone). So, even if unused, a cartridge could go bad. That is the theory, but, I've personally never encountered such problems--I've heard very old cartridges that still sound good after long storage.
My way of determining when a cartridge is beginning to go bad is to find the very few records that are challenging to track properly and listening for changes in the ability to handle the very few spots where distortion can be heard when everything is less than optimal.