The answer, obviously, is that their fate only matters if people are using them. And it's amazing what people are still using. A couple years ago Dell found a lawyer running a 22-year old MITS Altair as part of a contest and gave him a new duded-up system in exchange for it. The Altair was the platform on which Bill Gates and Paul Allen wrote their first Basic and founded Microsoft, way back when Ford was president and dinosaurs roamed the earth.
If people could still be running such an old piece of hardware relatively recently it should be no surprise that users are still running a lot of old DOS software, not to mention DOS itself. You can't buy DOS from Microsoft anymore; IBM still sells what they call "PC DOS 2000." What's left of DR-DOS is owned by DeviceLogics and is still for sale. There's also a kind of open-source DOS called OpenDOS.
It's platforms like DOS that take the longest to die. Consider another of the platforms allegedly in the dustbin of PC history: IBM's OS/2 Warp; IBM may want to kill it, but it just won't die. That's because a lot of people wrote a lot of software for it, it works, and they don't want to spend money on something new just because most other people have moved on to other "better" things.
And operating systems are not the only types of platforms. I think of a platform as a software system for which people write programs. Database software is the other major type of platform in this sense, and it's no surprise to find a lot of old database software still available. dBase, Clipper, and of course FoxPro, can all still be bought (dBase and Clipper still as DOS programs). Remember Framework, Ashton-Tate's entry in the DOS-based integrated program market of the mid 80's? It's still alive and well and still for sale at Solutions & Functions, Inc.
When a program like this shows such staying power I think it's reasonable to stick with it if it still does the job or if moving to a new system would be difficult or expensive. I think I would try to minimize the amount of new investment I did in it. But small companies like dBase Inc. probably provide the kind of service that bigger companies can't even imagine.
Of course, many old programs suffer a more ignominious fate. Framework may still be alive, but try to find any evidence of Lotus Symphony, one of its main competitors. You can't even find a user support site for the old Lotus programs, like the DOS versions of 1, 2, and 3. Some other dead programs, like Word Perfect 5.1 (one of the best computer programs ever written) still have active communities on the Web, like Ed Mendelson's WordPerfect for DOS Updated page.
Sometimes, software companies have to go away. Recently I read of how TurboPower Software is exiting the retail business and putting their products up in open source on Sourceforge.net. TurboPower makes components for Delphi developers. I was a TurboPower customer in the mid 80's when they wrote Turbo Pascal developer tools, and I used their products to write some fairly significant in-house corporate products. They always shipped source code with their products, but that's not the same as an open-source license. Developer tools like this are another good example of a platform, and programmers become dependent on them.
I know another small software company where the recent economic conditions have hurt the business and the owner/operator has gotten himself a day job. He's considering a similar move to put his main product in open source. The advantage of this is that it takes off the pressure to focus on the product but it doesn't completely abandon the existing customers. TurboPower is using the Mozilla license, which also gives them some options to re-enter some day with special rights.
This wasn't what open source was meant for, but it's not a bad plan B for a failing software company, assuming alternatives like selling the rights to the product aren't available. I suspect we will see a lot of projects like this go to open source, and perhaps many of the open-source Windows projects in the real world got their start this way.
One of the ironies of the long life of these ancient programs is that they were all written before the rise of the Internet, and therefore tend not to be capable of being in a position to have a security breach. Committing to an old program like this is a commitment to an old environment, a time when data sets were small, aesthetic sense was undemanding, and nobody expected programs to communicate. If you can still get your work done like that, then go for it.