One could have an unofficial death date by just ceasing to manufacture the hardware. If there are no PS2s or memory cards or controllers in stores I highly doubt any third party will bother making a game for a platform that is effectively out-of-print.
That hasn't stopped some companies from releasing titles for the Dreamcast. I think even the old Atari Jaguar is getting games... But of course, these games aren't appearing on store shelves either. AFAIK they are only available directly from the company.
But that works because (AFAIK) there are no licensing fees or developing kits needed to make games on those systems, and even if a company like Sony pulled the plug on their old hardware you can be sure they won't allow 3rd parties to publish games for it without collecting their fees.
Then again, after 20 years the patents expire and it becomes possible to publish games without licensing fees. At least in theory, a company could create and publish new NES games now without paying licensing fees because the patents to the NES are expired. In a year or two the SNES patents will also expire. But then again, these are cartridge systems so it would be costly to do that regardless, but still possible nonetheless.
Come to think of it, because of patent expiration 3rd party companies are legally allowed to produce the hardware as well as the games for said system. There are actually 3rd party knock-offs of NES consoles available, as well as the controllers and so forth. So not only do systems like this not die, but they actually witness a rebirth. it will be a long time before the PS2's patents expire, but we may see a similar thing happen then.