Earlier versions of Lightroom will not be able to read your Lightroom CC Catalog file.
The version of Lightroom you have when you stop your subscription will continue to function with some of the functions disabled.
I thing the things you need to know about Lightroom CC if you cancel your subscription are addressed in the article at the link below.
What happens to Lightroom after my membership ends?
[note]: We recently updated to Lightroom 6.0. When you’re subscription ends in Lr CC / Lr6, you will continue to have access to the Library, Slideshow, Web, Book and Print Modules as described below.
Since the launch of the Creative Cloud, Adobe has engaged in an ongoing dialog with the photographic community. We’ve tackled mobile workflows, provided ongoing enhancements and lastly, provided a membership plan tailor made for all levels of photographers. With the latest update to Lightroom 5.5 I believe we’ve also addressed a lingering concern in the community: What happens to my photographs after my membership ends? With Lightroom 5.5, at the end of a membership, the desktop application will continue to launch and provide access to the photographs managed within Lightroom as well as the Slideshow, Web, Book or Print creations that we know many photographers painstakingly create. The Develop and Map modules have been disabled in order to signal the end of the membership and the need to renew in order to receive Adobe’s continuous innovation in those areas. Access to Lightroom mobile workflows will also cease to function. We hope this meets the expectations of our customers and we look forward to an ongoing dialog.
Just to make sure I understand, "earlier versions will not be able to read your catalog".
But the next part sounds like the CC version of LR that I have at that time can read the catalog as library included, and I won't be able to use the develop, but all the filing and edits from before will be viewable. Is this right?
If/when your subscription ends, the Develop module will stop working. The Library module is still fully working, as is the Print module. Viewing and exporting will still work. Editing/changing the images will not work any more.
The catalogs are never forwards compatible. LR 5 cannot read the LR 6 catalogs. (LR 6 is LR CC 2015, just licensed differently to enable/disable a few UI features.) Assuming there is a LR 7, LR 6 will not be able to read the LR 7 catalogs.
Technically you can still edit your images after your subscription ends via Quick Develop in the Library. That would allow you to reset all the adjustments or make basic changes to the image.