what happens with old CMS/blog websites?
I think 99% is a very generous estimate, but that's beside the point. The majority of the sites that end up in the state you are referring to only last as long as their domain registrations (especially since most Wordpress or OSCommerce deployments are usually set up as the root domain and service the entirety of the web presence.) So generally speaking, if the domain itself is in a state of neglect and abandonment, the natural expiration process will decommission it and it will no longer be accessible in general.
As for locking down an entire, sitewide state on one of these CMS systems, it could in theory be possible if one removed all write privileges for all the server files and revoked every database user privilege except SELECT. In most cases this would defeat the purpose of leaving the software for CMS there at all, since none of the records would updatable any longer (items in the case of OSCommerce, posts in the case of Wordpress.) But this would be highly dependent on the environment required by the particular CMS, and Wordpress for one is pretty particular about read/write permissions to work at all. It would make for an interesting experiment, but probably isn't a practical solution for what you're describing.
Taking the rendered content and building a static mirror is another option, and can be pretty easily automated by writing a script that could get the HTML content of the rendered pages and building static, linked alternatives. But this too is a bit impractical, especially in the case of a search (since this by its very definition requires database access.)
In short, it's an interesting idea, but ultimately sites that are neglected and whose owners are not committed to sustaining proper updates are doomed to expiration, and the natural course of Internet business and domain registration pretty often Darwinizes them.
As an alternative solution (but I really don't know if its possible), is there any way to make a whole site into a read-only mode? I mean something like making the database read-only, the file system read-only, disabling the admin interface and all the comment fields and just leaving the site as an archive, the only dynamic part being the search function.
WP Super Cache has a "Lockdown" function — serving static HTML files for almost every visitor.It's not exactly what you're looking for, but a simple workaround, as I dont know a of a "read only" function for WordPress.