In mathematics and theoretical computer science, we read research papers primarily to find research questions to work on, or find techniques we can use to prove new theorems. What happens to a research area then when researchers go elsewhere?
In a response to a question about how can one contribute to mathematics, Bill Thurston notes that our knowledge of mathematics can deteriorate over time.
Mathematical understanding does not expand in a monotone direction. Our understanding frequently deteriorates as well. There are several obvious mechanisms of decay. The experts in a subject retire and die, or simply move on to other subjects and forget. Mathematics is commonly explained and recorded in symbolic and concrete forms that are easy to communicate, rather than in conceptual forms that are easy to understand once communicated. Translation in the direction conceptual -> concrete and symbolic is much easier than translation in the reverse direction, and symbolic forms often replaces the conceptual forms of understanding. And mathematical conventions and taken-for-granted knowledge change, so older texts may become hard to understand. In short, mathematics only exists in a living community of mathematicians that spreads understanding and breaths life into ideas both old and new.Once a research area fills out, researchers tend to move on to new and different ideas. Much of the research in the theoretical CS community in the 50's, 60's and 70's have been lost to journal articles, now nicely digitized but rarely downloaded.
What will happen with complexity classes once people stop studying them? You already don't see that many recent papers on complexity classes, even in the Computational Complexity Conference. A victim of our own success and failures: We settled most of the easy questions and the rest are very hard. As my generation retires, the classes may retire as well, outside of a couple of the biggies like P and NP. The old papers will still be out there, and you can always look up the classes in the zoo or on Wikipedia, but the understanding that goes with people studying these classes, and why we cared about them, may deteriorate just like computer programs that go unattended.