Others have mentioned the Attic, but I think the other crucial thing to be aware of here is that to the Apache Software Foundation, it's all about community. When a project wants to graduate from the Incubator and become a top-level project, no one asks what cutting-edge technology and new innovation is available for download, they ask about the health of the community. Are there enough active contributors? Do they come from a diverse set of employers? Is the mailing list traffic stable? Are you actually making releases and getting people to vote on things? There's no rule about how much work has to be in each release. That may, as you say, lead to bureaucratic ghost towns where the technological innovation has stopped, but that's why. That innovation is up to the individual communities. And as long as the community is there, Apache governance will not just barge in and tell you you're done.
I was on the PMC for a project that is now in the Attic. The project had been dead for a long time already. There was a discussion about killing it - only one company still had any interest and even they weren't actively doing anything. Apache wanted to see 3 active PMC members, so I volunteered to be one of the 3 if other people were interested, but then the next time they asked it was clear that no one was actually going to do anything. No releases. No mailing list traffic. No votes. THAT was what killed the project. The project had basically stopped innovating soon after graduating to a top-level project and had been that way for years - but there WAS active maintenance and an active mailing list of users. And Apache is fine with it - it is, as they say, a natural part of the life cycle of a project to go into maintenance mode.
As long as people are responding on the OpenOffice mailing list and releases are happening, Apache can consider that community alive. That they're not keeping up with LibreOffice or making major releases is not really a big concern. If the community really dies, yeah that's what the Attic is for.
That said if they don't plan to change, I'd love to see the community endorse LibreOffice as a successor.