Software goes stale all the time for many reasons. If you're not prepared to fix it or replace it yourself, you really shouldn't be using it.

In my experience, a lot of the projects with large numbers of CVEs also have a rather sprawling project with lots of things that can (and should) be disabled if they don't apply to your environment; most of the CVEs will happen in parts you don't use. (That's clearly not the case for all projects, openssl is a joy to have as a critical dependency, but there are some options now)

I don't see how a CLA materially affects this possibility, though. If my company sponsors a BSD-licensed open source project without enforcing a CLA and then decides that starting with the next major version, we're taking it closed source, the exact same thing you describe is just as likely to happen as with a CLA -- the deciding factor seems to me to be whether most of the development activity happening on the codebase is community-driven or driven by paid developers at the company. Conversely, if the community is active and doing a lot of major work already, and there are enough non-company developers with the time, interest, and skill to start and sustain a fork, they're going to do that with or without a CLA.