First, the main thing immediately would be money to keep it hosted. As for "maintaining" and moderating, give some users privileges to moderate. Well, good people. As for full admin status, that could take a little longer but maybe someone takes over. The important part is transferring the ownership of the accounts with any hosting service. There is no particular reason to actually shut down. If the forum's web software is robust, it should be able to stay operational 24/7 for considerable number of months as long as the hosting bills are paid for.
It's not like it is actually a fulltime job. Especially if the community self-moderate itself well by mere good behavior. Moderators can be appointed to keep the site clean of bot posts and such and even handle the day to day issues of resolving dramas that flares up every so often. People haven't offered to move the site and migrate it over for the following reasons: A) It might not be necessary to actually do that. B) Those are details to resolve after initial dialogue and obtaining the details of what needs to be done.
In general, it should not be that much of a problem to transfer account ownership with the hosting platforms regarding any sort of billing related matters. Even a general partnership group under some sort of organizational name operated by the community could be formed and funding be facilitated by the community for the community and then its obviously there may be additional persons appointed with admin level access to the forum and whatever else. Is it really necessary to migrate to a different web and domain hosting services?
