The problem of LiveJournal, fundamentally, is that it is a single organization, and therefore that it can be controlled, and it can be sold. Even though a non-profit or a co-op or what-have-you may be free of the dangers of being sold, it is still a single point of potential failure, and can be controlled.
I think the solution is to avoid this problem. Nobody's going to do something with my blog that I don't like, because it's my blog, on my domain name, on my server. (Well, okay, co-op server. But still.) Or, as a more mature model, there's Usenet -- for better or for ill, Usenet is what it is, and while it may fade away, it's not going to change.
I think the solution is to find a decentralized model for social friends-lock-able networking. A way that I can have my journal on my machine, and you can have your journal on your machine, and people can have journals on machines provided by the ElseJournal co-op or whatever is there, but with the ability to use my journal identity to see locked posts on your journal (if you want me to) and to comment there, and to have friendslists that link to other journals on other sites, and so forth.
I think the solution is to come up with an open standard for this sort of thing, and implementations of it, and maybe a co-op or two to provide services under it to users who don't want to run their own servers (which I suspect is the vast majority of us -- running something like this is work!).
And that way, whatever happens with the company, the network survives, and those of us who are affected can pick up our pieces and move them somewhere else and connect back to the network as a whole.
The OpenID project looks like a good start with a piece of this, but it's only a piece. What other pieces do we need? What projects are out there? A bit of looking into this seems to indicate that other people are working on it already, but I don't know details.